Finite Group Databasebeta

← Group #10828805

Character table — Group #10828805

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111111112222222222222222444444444444444444444444444444444488888888888888888888888888121212121212121224242424242424244848
order1222222234444444466666662244444444121212121212121212121212121212121212121212121212222444446666666612121212121212121212888888884444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11-1-11-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ4111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11-1-11-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ511111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ711111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11111-1-11111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1
χ91111111111-1-1-1-11111111111-1-111-1-111111111-1-1-1-11111-1-1-1-1111111111-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-11-1
χ101111111111-1-1-1-11111111111-1-111-1-111111111-1-1-1-11111-1-1-1-1111111111-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111-11
χ111111111111-1-1-1-11111111111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-111-1-1-1-1111111-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-11
χ121111111111-1-1-1-11111111111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1111-1
χ131111111111-1-1-1-11111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1111111111111-1111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-11
χ141111111111-1-1-1-11111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1111111111111-1111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-11-1
χ151111111111-1-1-1-11111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-111-1-1111-1
χ161111111111-1-1-1-11111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-111-1-1-11
χ17222222222-22222-2-2-22222222-2-222220000-2-2-2-222222222222200000000-200-20000-2-2-2-20000-2-200000000000000000000000000
χ18222222222-22222-2-2-22222222-2-2-2-2-2-20000-2-2-2-22222-2-2-2-2-2-2-2-20000000020020000-2-22200002200000000000000000000000000
χ19222222222-2-2-2-2-2-2-2-222222222222-2-20000-2-2-2-2-2-2-2-22222-2-2-2-200000000-2002000022-2-200002200000000000000000000000000
χ20222222222-2-2-2-2-2-2-2-2222222222-2-2220000-2-2-2-2-2-2-2-2-2-2-2-2222200000000200-2000022220000-2-200000000000000000000000000
χ2122222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000
χ2222222222-122222222-1-1-1-1-1-1-1222222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111112-2-22-2-2-2-2-1-1-1-11111-1-111111111000000000000000000
χ2322222222-122222222-1-1-1-1-1-1-122-2-2-2-22222-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-2-2-2-222-2-2-1-111111111-1-1-1-11111000000000000000000
χ2422222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-222-2-2-222-1-111-1-1-1-1111111-1-1-1-1000000000000000000
χ2522222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-222-2-22222-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-12-2-2-2-2-22211-1-11111111111-1-1-1-1000000000000000000
χ2622222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-222-2-2-2-2-2-2-1-1-1-11111-1-1-1-1111111111111222-222-2-211-1-1-1-1-1-111-1-1-1-11111000000000000000000
χ2722222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-2-2-2222222-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-2222-2-2-2-21111-1-1-1-1-1-111111111000000000000000000
χ2822222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-2-2-222-2-2-2-2-1-1-1-111111111-1-1-1-111111111-2-2-22222211111111-1-1-1-1-1-1-1-1-1-1000000000000000000
χ2922222222-1-22222-2-2-2-1-1-1-1-1-1-1-2-2222200001111-1-1-1-1-1-1-1-1-1-1-1-1−i3−i3−i3−i3i3i3i3i3-200-200001111−i3−i3i3i311−i3−i3i3i3−i3−i3i3i3000000000000000000
χ3022222222-1-22222-2-2-2-1-1-1-1-1-1-1-2-2222200001111-1-1-1-1-1-1-1-1-1-1-1-1i3i3i3i3−i3−i3−i3−i3-200-200001111i3i3−i3−i311i3i3−i3−i3i3i3−i3−i3000000000000000000
χ3122222222-1-22222-2-2-2-1-1-1-1-1-1-1-2-2-2-2-2-200001111-1-1-1-111111111−i3−i3−i3−i3i3i3i3i32002000011-1-1i3i3−i3−i3-1-1−i3−i3i3i3i3i3−i3−i3000000000000000000
χ3222222222-1-22222-2-2-2-1-1-1-1-1-1-1-2-2-2-2-2-200001111-1-1-1-111111111i3i3i3i3−i3−i3−i3−i32002000011-1-1−i3−i3i3i3-1-1i3i3−i3−i3−i3−i3i3i3000000000000000000
χ3322222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-12222-2-2000011111111-1-1-1-11111−i3−i3−i3−i3i3i3i3i3-20020000-1-111i3i3−i3−i3-1-1i3i3−i3−i3−i3−i3i3i3000000000000000000
χ3422222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-12222-2-2000011111111-1-1-1-11111i3i3i3i3−i3−i3−i3−i3-20020000-1-111−i3−i3i3i3-1-1−i3−i3i3i3i3i3−i3−i3000000000000000000
χ3522222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122-2-2220000111111111111-1-1-1-1−i3−i3−i3−i3i3i3i3i3200-20000-1-1-1-1−i3−i3i3i311i3i3−i3−i3i3i3−i3−i3000000000000000000
χ3622222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122-2-2220000111111111111-1-1-1-1i3i3i3i3−i3−i3−i3−i3200-20000-1-1-1-1i3i3−i3−i311−i3−i3i3i3−i3−i3i3i3000000000000000000
χ3722-222-2-2-22-200002-2222-2-22-2-20000002i2i−2i−2i22-2-20000000000002i2i−2i−2i2i2i−2i−2i00000000000000000000000000000022-2-2002i−2i000000
χ3822-222-2-2-22-200002-2222-2-22-2-20000002i2i−2i−2i22-2-20000000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000000000-2-22200−2i2i000000
χ3922-222-2-2-22-200002-2222-2-22-2-2000000−2i−2i2i2i22-2-2000000000000−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000022-2-200−2i2i000000
χ4022-222-2-2-22-200002-2222-2-22-2-2000000−2i−2i2i2i22-2-2000000000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000-2-222002i−2i000000
χ4122-2-2-222-2202i2i−2i−2i0002-22-2-22-2002i−2i2-2000000002i2i−2i−2i2i2i−2i−2i22-2-2000000000000000000000000000000000022−2−2−i2i2−i2i20000−i2i22−200
χ4222-2-2-222-2202i2i−2i−2i0002-22-2-22-2002i−2i2-2000000002i2i−2i−2i2i2i−2i−2i22-2-20000000000000000000000000000000000−2−222i2−i2i2−i20000i2−i2−2200
χ4322-2-2-222-2202i2i−2i−2i0002-22-2-22-200−2i2i-22000000002i2i−2i−2i−2i−2i2i2i-2-222000000000000000000000000000000000022−2−2−i2i2−i2i20000i2−i2−2200
χ4422-2-2-222-2202i2i−2i−2i0002-22-2-22-200−2i2i-22000000002i2i−2i−2i−2i−2i2i2i-2-2220000000000000000000000000000000000−2−222i2−i2i2−i20000−i2i22−200
χ4522-2-2-222-220−2i−2i2i2i0002-22-2-22-2002i−2i-2200000000−2i−2i2i2i2i2i−2i−2i-2-222000000000000000000000000000000000022−2−2i2−i2i2−i20000−i2i2−2200
χ4622-2-2-222-220−2i−2i2i2i0002-22-2-22-2002i−2i-2200000000−2i−2i2i2i2i2i−2i−2i-2-2220000000000000000000000000000000000−2−222−i2i2−i2i20000i2−i22−200
χ4722-2-2-222-220−2i−2i2i2i0002-22-2-22-200−2i2i2-200000000−2i−2i2i2i−2i−2i2i2i22-2-2000000000000000000000000000000000022−2−2i2−i2i2−i20000i2−i22−200
χ4822-2-2-222-220−2i−2i2i2i0002-22-2-22-200−2i2i2-200000000−2i−2i2i2i−2i−2i2i2i22-2-20000000000000000000000000000000000−2−222−i2i2−i2i20000−i2i2−2200
χ492-222-22-2-22-20000-222-2-2222-2-20000002i−2i2i−2i2-22-20000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000002-22-200002i−2i00000000
χ502-222-22-2-22-20000-222-2-2222-2-20000002i−2i2i−2i2-22-20000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000000000-22-220000−2i2i00000000
χ512-222-22-2-22-20000-222-2-2222-2-2000000−2i2i−2i2i2-22-2000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000002-22-20000−2i2i00000000
χ522-222-22-2-22-20000-222-2-2222-2-2000000−2i2i−2i2i2-22-2000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000-22-2200002i−2i00000000
χ532-2-22-2-222222-22-2-2-22-2-2-2-22222-200002-2-222-2-222-22-2000000002-2-222-2-2200002-2002-2000000002-22-20000000000000000000000
χ542-2-22-2-222222-22-2-2-22-2-2-2-22222-20000-222-22-2-222-22-200000000-222-2-222-20000-22002-200000000-22-220000000000000000000000
χ552-2-22-2-22222-22-22-2-22-2-2-2-2222-2200002-2-222-2-22-22-22000000002-2-222-2-220000-2200-2200000000-22-220000000000000000000000
χ562-2-22-2-22222-22-22-2-22-2-2-2-2222-220000-222-22-2-22-22-2200000000-222-2-222-200002-200-22000000002-22-20000000000000000000000
χ572-2-22-2-2222-22-22-222-2-2-2-2-2222-2200000000-222-22-22-2000000000000000002-20002-2-22002-22-20000002-22-2000000000000000000
χ582-2-22-2-2222-22-22-222-2-2-2-2-2222-2200000000-222-22-22-200000000000000000-22000-22-2200-22-22000000-22-22000000000000000000
χ592-2-22-2-2222-2-22-2222-2-2-2-2-22222-200000000-222-2-22-22000000000000000002-2000-222-2002-22-2000000-22-22000000000000000000
χ602-2-22-2-2222-2-22-2222-2-2-2-2-22222-200000000-222-2-22-2200000000000000000-220002-22-200-22-220000002-22-2000000000000000000
χ612-2-22-2-222-122-22-2-2-221111-1-1-12-200002-2-22-111-1-11-11−i3i3−i3i3−i3i3−i3i3-111-1-111-100002-200-11−i3i3−i3i3i3−i3−i3i3-11-11−i3i3i3−i3000000000000000000
χ622-2-22-2-222-122-22-2-2-221111-1-1-12-200002-2-22-111-1-11-11i3−i3i3−i3i3−i3i3−i3-111-1-111-100002-200-11i3−i3i3−i3−i3i3i3−i3-11-11i3−i3−i3i3000000000000000000
χ632-2-22-2-222-122-22-2-2-221111-1-1-12-20000-222-2-111-1-11-11−i3i3−i3i3−i3i3−i3i31-1-111-1-110000-2200-11−i3i3i3−i3−i3i3−i3i31-11-1i3−i3−i3i3000000000000000000
χ642-2-22-2-222-122-22-2-2-221111-1-1-12-20000-222-2-111-1-11-11i3−i3i3−i3i3−i3i3−i31-1-111-1-110000-2200-11i3−i3−i3i3i3−i3i3−i31-11-1−i3i3i3−i3000000000000000000
χ652-2-22-2-222-12-22-22-2-221111-1-1-1-2200002-2-22-111-11-11-1−i3i3−i3i3i3−i3i3−i3-111-1-111-10000-22001-1−i3i3i3−i3−i3i3i3−i31-11-1−i3i3i3−i3000000000000000000
χ662-2-22-2-222-12-22-22-2-221111-1-1-1-2200002-2-22-111-11-11-1i3−i3i3−i3−i3i3−i3i3-111-1-111-10000-22001-1i3−i3−i3i3i3−i3−i3i31-11-1i3−i3−i3i3000000000000000000
χ672-2-22-2-222-12-22-22-2-221111-1-1-1-220000-222-2-111-11-11-1−i3i3−i3i3i3−i3i3−i31-1-111-1-1100002-2001-1−i3i3−i3i3i3−i3i3−i3-11-11i3−i3−i3i3000000000000000000
χ682-2-22-2-222-12-22-22-2-221111-1-1-1-220000-222-2-111-11-11-1i3−i3i3−i3−i3i3−i3i31-1-111-1-1100002-2001-1i3−i3i3−i3−i3i3−i3i3-11-11−i3i3i3−i3000000000000000000
χ692-2-22-2-222-1-22-22-222-21111-1-1-1-22000000001-1-11-11-11−i3i3−i3i3−i3i3−i3i3−i3i3i3−i3i3−i3−i3i302-20002-21-1i3−i3-11-11i3−i3−i3i3i3−i3-11-11000000000000000000
χ702-2-22-2-222-1-22-22-222-21111-1-1-1-22000000001-1-11-11-11−i3i3−i3i3−i3i3−i3i3i3−i3−i3i3−i3i3i3−i30-22000-221-1i3−i31-11-1i3−i3i3−i3−i3i31-11-1000000000000000000
χ712-2-22-2-222-1-22-22-222-21111-1-1-1-22000000001-1-11-11-11i3−i3i3−i3i3−i3i3−i3−i3i3i3−i3i3−i3−i3i30-22000-221-1−i3i31-11-1−i3i3−i3i3i3−i31-11-1000000000000000000
χ722-2-22-2-222-1-22-22-222-21111-1-1-1-22000000001-1-11-11-11i3−i3i3−i3i3−i3i3−i3i3−i3−i3i3−i3i3i3−i302-20002-21-1−i3i3-11-11−i3i3i3−i3−i3i3-11-11000000000000000000
χ732-2-22-2-222-1-2-22-2222-21111-1-1-12-2000000001-1-111-11-1−i3i3−i3i3i3−i3i3−i3−i3i3i3−i3i3−i3−i3i30-220002-2-11i3−i31-11-1−i3i3i3−i3−i3i3-11-11000000000000000000
χ742-2-22-2-222-1-2-22-2222-21111-1-1-12-2000000001-1-111-11-1−i3i3−i3i3i3−i3i3−i3i3−i3−i3i3−i3i3i3−i302-2000-22-11i3−i3-11-11−i3i3−i3i3i3−i31-11-1000000000000000000
χ752-2-22-2-222-1-2-22-2222-21111-1-1-12-2000000001-1-111-11-1i3−i3i3−i3−i3i3−i3i3−i3i3i3−i3i3−i3−i3i302-2000-22-11−i3i3-11-11i3−i3i3−i3−i3i31-11-1000000000000000000
χ762-2-22-2-222-1-2-22-2222-21111-1-1-12-2000000001-1-111-11-1i3−i3i3−i3−i3i3−i3i3i3−i3−i3i3−i3i3i3−i30-220002-2-11−i3i31-11-1i3−i3−i3i3i3−i3-11-11000000000000000000
χ77444-4-4-4-444000000004-4-44-4-440000000000000000000000000000000000000000000000000000000000000000−2i22i22i2−2i20000000000
χ78444-4-4-4-444000000004-4-44-4-4400000000000000000000000000000000000000000000000000000000000000002i2−2i2−2i22i20000000000
χ7944-444-4-4-4440000-44-444-4-44-4-40000000000-4-4440000000000000000000000000000000000000000000000000000000000000000
χ8044-444-4-4-4-240000-44-4-2-222-222000000000022-2-20000000000002323−23−23−23−23232300000000000000000000000000000000000000000000
χ8144-444-4-4-4-240000-44-4-2-222-222000000000022-2-2000000000000−23−2323232323−23−2300000000000000000000000000000000000000000000
χ8244-444-4-4-4-2-400004-44-2-222-2220000004i4i−4i−4i-2-222000000000000−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000000000000000
χ8344-444-4-4-4-2-400004-44-2-222-222000000−4i−4i4i4i-2-2220000000000002i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000000000000000
χ8444-4-4-444-4-204i4i−4i−4i000-22-222-22004i−4i4-400000000−2i−2i2i2i−2i−2i2i2i-2-2220000000000000000000000000000000000000000000000000000
χ8544-4-4-444-4-204i4i−4i−4i000-22-222-2200−4i4i-4400000000−2i−2i2i2i2i2i−2i−2i22-2-20000000000000000000000000000000000000000000000000000
χ8644-4-4-444-4-20−4i−4i4i4i000-22-222-22004i−4i-44000000002i2i−2i−2i−2i−2i2i2i22-2-20000000000000000000000000000000000000000000000000000
χ8744-4-4-444-4-20−4i−4i4i4i000-22-222-2200−4i4i4-4000000002i2i−2i−2i2i2i−2i−2i-2-2220000000000000000000000000000000000000000000000000000
χ884-444-44-4-44400004-4-4-4-4444-4-40000000000-44-440000000000000000000000000000000000000000000000000000000000000000
χ894-444-44-4-4-2400004-4-422-2-2-22200000000002-22-200000000000023−2323−23−2323−232300000000000000000000000000000000000000000000
χ904-444-44-4-4-2400004-4-422-2-2-22200000000002-22-2000000000000−2323−232323−2323−2300000000000000000000000000000000000000000000
χ914-444-44-4-4-2-40000-44422-2-2-2220000004i−4i4i−4i-22-22000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000000000000000
χ924-444-44-4-4-2-40000-44422-2-2-222000000−4i4i−4i4i-22-220000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000000000000000
χ934-44-44-44-4404i−4i−4i4i000-44-44-44-4000000000000004i−4i−4i4i000000000000000000000000000000000000000000000000000000000000
χ944-44-44-44-440−4i4i4i−4i000-44-44-44-400000000000000−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000
χ954-44-44-44-4-204i−4i−4i4i0002-22-22-2200000000000000−2i2i2i−2i23−23−2323−2i32i32i3−2i30000000000000000000000000000000000000000000000000000
χ964-44-44-44-4-204i−4i−4i4i0002-22-22-2200000000000000−2i2i2i−2i−232323−232i3−2i3−2i32i30000000000000000000000000000000000000000000000000000
χ974-44-44-44-4-20−4i4i4i−4i0002-22-22-22000000000000002i−2i−2i2i23−23−23232i3−2i3−2i32i30000000000000000000000000000000000000000000000000000
χ984-44-44-44-4-20−4i4i4i−4i0002-22-22-22000000000000002i−2i−2i2i−232323−23−2i32i32i3−2i30000000000000000000000000000000000000000000000000000
χ994-4-4-444-44400000000-444-4-4-4400000000000000000000000000000000000000000000000000000000000022−22−222200000000000000
χ1004-4-4-444-44400000000-444-4-4-44000000000000000000000000000000000000000000000000000000000000−222222−2200000000000000
χ101888-8-8-8-88-400000000-444-444-4000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1028-8-8-888-88-4000000004-4-4444-4000000000000000000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).