Finite Group Databasebeta

← Group #10849345

Character table — Group #10849345

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222444444444444444444444444444444444444888888888888888888888888882424242424242424242424244848
order12222222344446666666444444444444121212121212121212121212121212121212121212121212224444446666121212121212121212121212121244448888888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ41111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ51111111111111111111111-1-111-1-111111111-1-1-1-11111-1-1-1-111111111-1-1-111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1
χ61111111111111111111111-1-111-1-111111111-1-1-1-11111-1-1-1-111111111-1-1-111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ71111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-11111-1-111-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ81111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-11111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111
χ911111111111111111111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-111-1-111-1-11-1
χ1011111111111111111111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1111-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-111-1-111-11
χ1111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-111-1-111111-1-1-1-1111111-1-1-1-111-1-1-1-111-1-1111-1
χ1211111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-111-1-111111-1-1-1-1111111-1-1-1-1-1-11111-1-111-1-1-11
χ1311111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111-11
χ1411111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-11-1
χ1511111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-111-1-1-1-11111111111-1-1-1-11111-1-1-11
χ1611111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-111-1-1-1-111111111-1-11111-1-1-1-1111-1
χ17222222222-2-2-2-222222222222-2-222000022222222-2-2-2-222220000000000-20000-20000-2-2-2-2-2-20000000000000000000000
χ18222222222-2-2-2-2222222222-2-2-2-2-2-200002222-2-2-2-2-2-2-2-2-2-2-2-20000000000200002000022-2-2220000000000000000000000
χ19222222222-2-2-2-22222222-2-22222-2-20000-2-2-2-22222-2-2-2-2-2-2-2-2000000000020000-200002222-2-20000000000000000000000
χ20222222222-2-2-2-22222222-2-2-2-222220000-2-2-2-2-2-2-2-2-2-2-2-222220000000000-2000020000-2-222220000000000000000000000
χ2122222222-12222-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000
χ2222222222-12222-1-1-1-1-1-1-122222222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-2-22-2-2-2-221111-1-1-1-1-1-11111111100000000000000
χ2322222222-12222-1-1-1-1-1-1-122-2-222-2-22222-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-2-2-222-2-2-2111111-1-111-1-1-1-1111100000000000000
χ2422222222-12222-1-1-1-1-1-1-122-2-222-2-2-2-2-2-2-1-1-1-11111-1-1-1-111111111111122-2-2-222-2-1-1-1-111-1-1111111-1-1-1-100000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-222-2-2-2-222221111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-2-2-2-2-222211111111-1-11111-1-1-1-100000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-222-2-2-2-2-2-2-2-21111-1-1-1-1-1-1-1-111111111111122-222-2-22-1-1-1-11111-1-1-1-1-1-1111100000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-222222211111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222-2-2-2-2-2-1-1-1-1-1-111111111111100000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-222-2-2-2-211111111-1-1-1-1-1-1-1-111111111-2-222222-21111-1-11111-1-1-1-1-1-1-1-100000000000000
χ2922222222-1-2-2-2-2-1-1-1-1-1-1-12222-2-2220000-1-1-1-1-1-1-1-11111-1-1-1-1−i3−i3−i3−i3i3i3i3i300-20000-2−i3−i3i3i3111111−i3−i3i3i3−i3−i3i3i300000000000000
χ3022222222-1-2-2-2-2-1-1-1-1-1-1-12222-2-2220000-1-1-1-1-1-1-1-11111-1-1-1-1i3i3i3i3−i3−i3−i3−i300-20000-2i3i3−i3−i3111111i3i3−i3−i3i3i3−i3−i300000000000000
χ3122222222-1-2-2-2-2-1-1-1-1-1-1-122-2-2-2-2-2-20000-1-1-1-1111111111111−i3−i3−i3−i3i3i3i3i300200002i3i3−i3−i3-1-111-1-1−i3−i3i3i3i3i3−i3−i300000000000000
χ3222222222-1-2-2-2-2-1-1-1-1-1-1-122-2-2-2-2-2-20000-1-1-1-1111111111111i3i3i3i3−i3−i3−i3−i300200002−i3−i3i3i3-1-111-1-1i3i3−i3−i3−i3−i3i3i300000000000000
χ3322222222-1-2-2-2-2-1-1-1-1-1-1-1-2-22222-2-200001111-1-1-1-111111111−i3−i3−i3−i3i3i3i3i30020000-2i3i3−i3−i3-1-1-1-111i3i3−i3−i3−i3−i3i3i300000000000000
χ3422222222-1-2-2-2-2-1-1-1-1-1-1-1-2-22222-2-200001111-1-1-1-111111111i3i3i3i3−i3−i3−i3−i30020000-2−i3−i3i3i3-1-1-1-111−i3−i3i3i3i3i3−i3−i300000000000000
χ3522222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2-2-222220000111111111111-1-1-1-1−i3−i3−i3−i3i3i3i3i300-200002−i3−i3i3i311-1-1-1-1i3i3−i3−i3i3i3−i3−i300000000000000
χ3622222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2-2-222220000111111111111-1-1-1-1i3i3i3i3−i3−i3−i3−i300-200002i3i3−i3−i311-1-1-1-1−i3−i3i3i3−i3−i3i3i300000000000000
χ3722-2-222-2-22-22-2222-2-2-22-2000000002i2i−2i−2i0000000022-2-200002i2i−2i−2i2i2i−2i−2i00000000000000000000000000002-2002i−2i000000
χ3822-2-222-2-22-22-2222-2-2-22-2000000002i2i−2i−2i0000000022-2-200002i2i−2i−2i2i2i−2i−2i0000000000000000000000000000-2200−2i2i000000
χ3922-2-222-2-22-22-2222-2-2-22-200000000−2i−2i2i2i0000000022-2-20000−2i−2i2i2i−2i−2i2i2i00000000000000000000000000002-200−2i2i000000
χ4022-2-222-2-22-22-2222-2-2-22-200000000−2i−2i2i2i0000000022-2-20000−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000-22002i−2i000000
χ412-22-22-22-22-2-222-2-222-22-2000000002i−2i2i−2i000000002-22-200002i−2i2i−2i2i−2i2i−2i000000000000000000000000002-2002i−2i00000000
χ422-22-22-22-22-2-222-2-222-22-2000000002i−2i2i−2i000000002-22-200002i−2i2i−2i2i−2i2i−2i00000000000000000000000000-2200−2i2i00000000
χ432-22-22-22-22-2-222-2-222-22-200000000−2i2i−2i2i000000002-22-20000−2i2i−2i2i−2i2i−2i2i000000000000000000000000002-200−2i2i00000000
χ442-22-22-22-22-2-222-2-222-22-200000000−2i2i−2i2i000000002-22-20000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000-22002i−2i00000000
χ452-2-222-2-2222-2-22-2-2-2-22222-2002-2002-2-2222-2-200002-2-2200002-2-222-2-220002-20000000002-2002-22-2000000000000000000
χ462-2-222-2-2222-2-22-2-2-2-22222-2002-200-222-222-2-200002-2-220000-222-2-222-2000-220000000002-200-22-22000000000000000000
χ472-2-222-2-2222-2-22-2-2-2-2222-2200-22002-2-22-2-22200002-2-2200002-2-222-2-22000-22000000000-2200-22-22000000000000000000
χ482-2-222-2-2222-2-22-2-2-2-2222-2200-2200-222-2-2-22200002-2-220000-222-2-222-20002-2000000000-22002-22-2000000000000000000
χ492-2-222-2-222-222-2-2-2-2-22222-200-2200000022-2-20000-222-20000000000002-20002-202-22-200-220000002-22-200000000000000
χ502-2-222-2-222-222-2-2-2-2-22222-200-2200000022-2-20000-222-2000000000000-22000-220-22-2200-22000000-22-2200000000000000
χ512-2-222-2-222-222-2-2-2-2-2222-22002-2000000-2-2220000-222-20000000000002-2000-2202-22-2002-2000000-22-2200000000000000
χ522-2-222-2-222-222-2-2-2-2-2222-22002-2000000-2-2220000-222-2000000000000-220002-20-22-22002-20000002-22-200000000000000
χ532-2-222-2-22-12-2-221111-1-1-12-2002-2002-2-22-1-111−i3−i3i3i3-111-1−i3−i3i3i3-111-1-111-10002-2000−i3i3i3−i3−i3i3-11−i3i3-11-11−i3i3i3−i300000000000000
χ542-2-222-2-22-12-2-221111-1-1-12-2002-2002-2-22-1-111i3i3−i3−i3-111-1i3i3−i3−i3-111-1-111-10002-2000i3−i3−i3i3i3−i3-11i3−i3-11-11i3−i3−i3i300000000000000
χ552-2-222-2-22-12-2-221111-1-1-12-2002-200-222-2-1-111−i3−i3i3i3-111-1−i3−i3i3i31-1-111-1-11000-22000i3−i3−i3i3−i3i3-11−i3i31-11-1i3−i3−i3i300000000000000
χ562-2-222-2-22-12-2-221111-1-1-12-2002-200-222-2-1-111i3i3−i3−i3-111-1i3i3−i3−i31-1-111-1-11000-22000−i3i3i3−i3i3−i3-11i3−i31-11-1−i3i3i3−i300000000000000
χ572-2-222-2-22-12-2-221111-1-1-1-2200-22002-2-2211-1-1−i3−i3i3i3-111-1i3i3−i3−i3-111-1-111-1000-22000i3−i3−i3i3i3−i31-1−i3i31-11-1−i3i3i3−i300000000000000
χ582-2-222-2-22-12-2-221111-1-1-1-2200-22002-2-2211-1-1i3i3−i3−i3-111-1−i3−i3i3i3-111-1-111-1000-22000−i3i3i3−i3−i3i31-1i3−i31-11-1i3−i3−i3i300000000000000
χ592-2-222-2-22-12-2-221111-1-1-1-2200-2200-222-211-1-1−i3−i3i3i3-111-1i3i3−i3−i31-1-111-1-110002-2000−i3i3i3−i3i3−i31-1−i3i3-11-11i3−i3−i3i300000000000000
χ602-2-222-2-22-12-2-221111-1-1-1-2200-2200-222-211-1-1i3i3−i3−i3-111-1−i3−i3i3i31-1-111-1-110002-2000i3−i3−i3i3−i3i31-1i3−i3-11-11−i3i3i3−i300000000000000
χ612-2-222-2-22-1-222-21111-1-1-12-200-22000000-1-111−i3−i3i3i31-1-11−i3−i3i3i3−i3i3i3−i3i3−i3−i3i32-20002-20-11-11i3−i31-1i3−i3−i3i3i3−i3-11-1100000000000000
χ622-2-222-2-22-1-222-21111-1-1-12-200-22000000-1-111−i3−i3i3i31-1-11−i3−i3i3i3i3−i3−i3i3−i3i3i3−i3-22000-2201-11-1i3−i31-1i3−i3i3−i3−i3i31-11-100000000000000
χ632-2-222-2-22-1-222-21111-1-1-12-200-22000000-1-111i3i3−i3−i31-1-11i3i3−i3−i3−i3i3i3−i3i3−i3−i3i3-22000-2201-11-1−i3i31-1−i3i3−i3i3i3−i31-11-100000000000000
χ642-2-222-2-22-1-222-21111-1-1-12-200-22000000-1-111i3i3−i3−i31-1-11i3i3−i3−i3i3−i3−i3i3−i3i3i3−i32-20002-20-11-11−i3i31-1−i3i3i3−i3−i3i3-11-1100000000000000
χ652-2-222-2-22-1-222-21111-1-1-1-22002-200000011-1-1−i3−i3i3i31-1-11i3i3−i3−i3−i3i3i3−i3i3−i3−i3i3-220002-201-11-1−i3i3-11i3−i3i3−i3−i3i3-11-1100000000000000
χ662-2-222-2-22-1-222-21111-1-1-1-22002-200000011-1-1−i3−i3i3i31-1-11i3i3−i3−i3i3−i3−i3i3−i3i3i3−i32-2000-220-11-11−i3i3-11i3−i3−i3i3i3−i31-11-100000000000000
χ672-2-222-2-22-1-222-21111-1-1-1-22002-200000011-1-1i3i3−i3−i31-1-11−i3−i3i3i3−i3i3i3−i3i3−i3−i3i32-2000-220-11-11i3−i3-11−i3i3i3−i3−i3i31-11-100000000000000
χ682-2-222-2-22-1-222-21111-1-1-1-22002-200000011-1-1i3i3−i3−i31-1-11−i3−i3i3i3i3−i3−i3i3−i3i3i3−i3-220002-201-11-1i3−i3-11−i3i3−i3i3i3−i3-11-1100000000000000
χ69444-4-4-4-44400004-44-4-4-44004i−4i0000000000004i−4i4i−4i00000000000000000000000000000000000000000000000000000000
χ70444-4-4-4-44400004-44-4-4-4400−4i4i000000000000−4i4i−4i4i00000000000000000000000000000000000000000000000000000000
χ71444-4-4-4-44-20000-22-2222-2004i−4i0000000023−2323−23−2i2i−2i2i0000−2i32i3−2i32i3000000000000000000000000000000000000000000000000
χ72444-4-4-4-44-20000-22-2222-2004i−4i00000000−2323−2323−2i2i−2i2i00002i3−2i32i3−2i3000000000000000000000000000000000000000000000000
χ73444-4-4-4-44-20000-22-2222-200−4i4i0000000023−2323−232i−2i2i−2i00002i3−2i32i3−2i3000000000000000000000000000000000000000000000000
χ74444-4-4-4-44-20000-22-2222-200−4i4i00000000−2323−23232i−2i2i−2i0000−2i32i3−2i32i3000000000000000000000000000000000000000000000000
χ7544-44-4-44-4400004-4-444-4-400000000000000000000000000000000000000000000000000000000000000000000000022−2200
χ7644-44-4-44-4400004-4-444-4-4000000000000000000000000000000000000000000000000000000000000000000000000−222200
χ7744-4-444-4-444-44-444-4-4-44-400000000000000000000-4-4440000000000000000000000000000000000000000000000000000
χ7844-4-444-4-4-24-44-4-2-2222-220000000000000000000022-2-200002323−23−23−23−2323230000000000000000000000000000000000000000
χ7944-4-444-4-4-24-44-4-2-2222-220000000000000000000022-2-20000−23−2323232323−23−230000000000000000000000000000000000000000
χ8044-4-444-4-4-2-44-44-2-2222-22000000004i4i−4i−4i00000000-2-2220000−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000000000
χ8144-4-444-4-4-2-44-44-2-2222-2200000000−4i−4i4i4i00000000-2-22200002i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000000000
χ824-444-44-4-440000-444-44-4-4000000000000000000000000000000000000000000000000000000000000000000000022−220000
χ834-444-44-4-440000-444-44-4-40000000000000000000000000000000000000000000000000000000000000000000000−22220000
χ844-44-44-44-4444-4-4-4-444-44-400000000000000000000-44-440000000000000000000000000000000000000000000000000000
χ854-44-44-44-4-244-4-422-2-22-22000000000000000000002-22-2000023−2323−23−2323−23230000000000000000000000000000000000000000
χ864-44-44-44-4-244-4-422-2-22-22000000000000000000002-22-20000−2323−232323−2323−230000000000000000000000000000000000000000
χ874-44-44-44-4-2-4-44422-2-22-22000000004i−4i4i−4i00000000-22-220000−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000000000
χ884-44-44-44-4-2-4-44422-2-22-2200000000−4i4i−4i4i00000000-22-2200002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000000000
χ894-4-4-4-444440000-44-44-4-440000004-400000000000000004-4-44000000000000000000000000000000000000000000000000
χ904-4-4-4-444440000-44-44-4-44000000-440000000000000000-444-4000000000000000000000000000000000000000000000000
χ914-4-4-4-4444-200002-22-222-20000004-4000023−23−232323−23−23230000-222-2000000000000000000000000000000000000000000000000
χ924-4-4-4-4444-200002-22-222-20000004-40000−232323−23−232323−230000-222-2000000000000000000000000000000000000000000000000
χ934-4-4-4-4444-200002-22-222-2000000-44000023−23−2323−232323−2300002-2-22000000000000000000000000000000000000000000000000
χ944-4-4-4-4444-200002-22-222-2000000-440000−232323−2323−23−232300002-2-22000000000000000000000000000000000000000000000000
χ9588-88-8-88-8-40000-444-4-4440000000000000000000000000000000000000000000000000000000000000000000000000000
χ968-888-88-8-8-400004-4-44-4440000000000000000000000000000000000000000000000000000000000000000000000000000

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