Finite Group Databasebeta

← Group #10824852

Character table — Group #10824852

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222222222224444444444448888888888888888888888888888888888881212121212121212242424242424242424242424
order1222222234444444444446666666121212121212121212121212244444444444661212121212121212121212121212121212121212121288888888224444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-11-1-1-1-11-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ4111111111111111111111111111111111111111111-1-11-1-1-1-11-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ51111111111111111111111111111111111111111-1-111-1-1-111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1
χ61111111111111111111111111111111111111111-1-111-1-1-111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111
χ71111111111111111111111111111111111111111-1-1-1-1-111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-11111-1-1-1-1-1-1
χ81111111111111111111111111111111111111111-1-1-1-1-111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1111111
χ9111111111-1-1-1-111-1-1-1-1111111111-1-1-1-11111-1-1-1-11-111111-1-1-1-1-111-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-1
χ10111111111-1-1-1-111-1-1-1-1111111111-1-1-1-11111-1-1-1-11-111111-1-1-1-1-111-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-1-111
χ11111111111-1-1-1-111-1-1-1-1111111111-1-1-1-11111-1-1-1-11-1-1-11-1-111-11111-1-1-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-11111-1-1
χ12111111111-1-1-1-111-1-1-1-1111111111-1-1-1-11111-1-1-1-11-1-1-11-1-111-11111-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-111
χ13111111111-1-1-1-111-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1111-1-1-1-1-1111-1-1111111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111
χ14111111111-1-1-1-111-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1111-1-1-1-1-1111-1-1111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1
χ15111111111-1-1-1-111-1-1-1-1111111111-1-1-1-11111-1-1-1-1-11-1-1-111111-1-1-1-111-1-1-1-11111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111
χ16111111111-1-1-1-111-1-1-1-1111111111-1-1-1-11111-1-1-1-1-11-1-1-111111-1-1-1-111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1
χ172222222222222-2-2-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-22-200-2000020022-2-200000000-2-2220000000000000000000000000000
χ182222222222222-2-2-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-2-220020000-200-2-2220000000022-2-20000000000000000000000000000
χ19222222222-2-2-2-2-2-22222-2-22222222-2-2-2-2-2-2-2-222222200-20000-200222200000000-2-2-2-20000000000000000000000000000
χ20222222222-2-2-2-2-2-22222-2-22222222-2-2-2-2-2-2-2-22222-2-20020000200-2-2-2-20000000022220000000000000000000000000000
χ2122222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ2222222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-22-2-2-2-22-2-2-1-1-1-111111111-1-1-1-11111111100000000000000000000
χ2322222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-2-222-2-2-21111-1-1-1-1-1-1-1-111111111111100000000000000000000
χ2422222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-222-2-2-2221111111111111111-1-1-1-1-1-1-1-100000000000000000000
χ2522222222-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1111111112-200-20000200-1-111−i3−i3i3i3−i3−i3i3i311-1-1−i3−i3i3i3−i3−i3i3i300000000000000000000
χ2622222222-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1111111112-200-20000200-1-111i3i3−i3−i3i3i3−i3−i311-1-1i3i3−i3−i3i3i3−i3−i300000000000000000000
χ2722222222-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-111111111-220020000-20011-1-1−i3−i3i3i3−i3−i3i3i3-1-111i3i3−i3−i3i3i3−i3−i300000000000000000000
χ2822222222-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-111111111-220020000-20011-1-1i3i3−i3−i3i3i3−i3−i3-1-111−i3−i3i3i3−i3−i3i3i300000000000000000000
χ2922222222-1-2-2-2-222-2-2-2-222-1-1-1-1-1-1-11111-1-1-1-111112-222222-2-2-2-2-2-1-111-1-1-1-11111-1-111-1-1-1-1111100000000000000000000
χ3022222222-1-2-2-2-222-2-2-2-222-1-1-1-1-1-1-11111-1-1-1-111112-2-2-22-2-222-222-1-1111111-1-1-1-1-1-1111111-1-1-1-100000000000000000000
χ3122222222-1-2-2-2-222-2-2-2-222-1-1-1-1-1-1-11111-1-1-1-11111-2222-2-2-2-2-222211-1-1-1-1-1-1111111-1-11111-1-1-1-100000000000000000000
χ3222222222-1-2-2-2-222-2-2-2-222-1-1-1-1-1-1-11111-1-1-1-11111-22-2-2-222222-2-211-1-11111-1-1-1-111-1-1-1-1-1-1111100000000000000000000
χ3322222222-1-2-2-2-2-2-22222-2-2-1-1-1-1-1-1-111111111-1-1-1-12200-20000-200-1-1-1-1−i3−i3i3i3i3i3−i3−i31111−i3−i3i3i3i3i3−i3−i300000000000000000000
χ3422222222-1-2-2-2-2-2-22222-2-2-1-1-1-1-1-1-111111111-1-1-1-12200-20000-200-1-1-1-1i3i3−i3−i3−i3−i3i3i31111i3i3−i3−i3−i3−i3i3i300000000000000000000
χ3522222222-1-2-2-2-2-2-22222-2-2-1-1-1-1-1-1-111111111-1-1-1-1-2-200200002001111−i3−i3i3i3i3i3−i3−i3-1-1-1-1i3i3−i3−i3−i3−i3i3i300000000000000000000
χ3622222222-1-2-2-2-2-2-22222-2-2-1-1-1-1-1-1-111111111-1-1-1-1-2-200200002001111i3i3−i3−i3−i3−i3i3i3-1-1-1-1−i3−i3i3i3i3i3−i3−i300000000000000000000
χ3722-2-22-22-222i2i−2i−2i2-22i2i−2i−2i2-22-22-2-22-22i2i−2i−2i22-2-22i2i−2i−2i00000000000000000000000000000000000000000000002i−2i2-2000000
χ3822-2-22-22-222i2i−2i−2i2-22i2i−2i−2i2-22-22-2-22-22i2i−2i−2i22-2-22i2i−2i−2i0000000000000000000000000000000000000000000000−2i2i-22000000
χ3922-2-22-22-222i2i−2i−2i-22−2i−2i2i2i-222-22-2-22-22i2i−2i−2i-2-222−2i−2i2i2i000000000000000000000000000000000000000000002-200002i−2i0000
χ4022-2-22-22-222i2i−2i−2i-22−2i−2i2i2i-222-22-2-22-22i2i−2i−2i-2-222−2i−2i2i2i00000000000000000000000000000000000000000000-220000−2i2i0000
χ4122-2-22-22-22−2i−2i2i2i2-2−2i−2i2i2i2-22-22-2-22-2−2i−2i2i2i22-2-2−2i−2i2i2i00000000000000000000000000000000000000000000002i−2i-22000000
χ4222-2-22-22-22−2i−2i2i2i2-2−2i−2i2i2i2-22-22-2-22-2−2i−2i2i2i22-2-2−2i−2i2i2i0000000000000000000000000000000000000000000000−2i2i2-2000000
χ4322-2-22-22-22−2i−2i2i2i-222i2i−2i−2i-222-22-2-22-2−2i−2i2i2i-2-2222i2i−2i−2i000000000000000000000000000000000000000000002-20000−2i2i0000
χ4422-2-22-22-22−2i−2i2i2i-222i2i−2i−2i-222-22-2-22-2−2i−2i2i2i-2-2222i2i−2i−2i00000000000000000000000000000000000000000000-2200002i−2i0000
χ452-22-222-2-222i−2i2i−2i2-22i−2i2i−2i-22-22-22-22-22i−2i2i−2i2-22-22i−2i2i−2i000002-20002i−2i00000000000000002-22-22i−2i2i−2i00000000000000000000
χ462-22-222-2-222i−2i2i−2i2-22i−2i2i−2i-22-22-22-22-22i−2i2i−2i2-22-22i−2i2i−2i00000-22000−2i2i0000000000000000-22-22−2i2i−2i2i00000000000000000000
χ472-22-222-2-222i−2i2i−2i-22−2i2i−2i2i2-2-22-22-22-22i−2i2i−2i-22-22−2i2i−2i2i002-20002i−2i00000002-22-22i−2i2i−2i00000000000000000000000000000000
χ482-22-222-2-222i−2i2i−2i-22−2i2i−2i2i2-2-22-22-22-22i−2i2i−2i-22-22−2i2i−2i2i00-22000−2i2i0000000-22-22−2i2i−2i2i00000000000000000000000000000000
χ492-22-222-2-22−2i2i−2i2i2-2−2i2i−2i2i-22-22-22-22-2−2i2i−2i2i2-22-2−2i2i−2i2i000002-2000−2i2i00000000000000002-22-2−2i2i−2i2i00000000000000000000
χ502-22-222-2-22−2i2i−2i2i2-2−2i2i−2i2i-22-22-22-22-2−2i2i−2i2i2-22-2−2i2i−2i2i00000-220002i−2i0000000000000000-22-222i−2i2i−2i00000000000000000000
χ512-22-222-2-22−2i2i−2i2i-222i−2i2i−2i2-2-22-22-22-2−2i2i−2i2i-22-222i−2i2i−2i002-2000−2i2i00000002-22-2−2i2i−2i2i00000000000000000000000000000000
χ522-22-222-2-22−2i2i−2i2i-222i−2i2i−2i2-2-22-22-22-2−2i2i−2i2i-22-222i−2i2i−2i00-220002i−2i0000000-22-222i−2i2i−2i00000000000000000000000000000000
χ532-22-222-2-2-12i−2i2i−2i2-22i−2i2i−2i-221-11-11-11−ii−ii-11-11−ii−ii000002-20002i−2i−i3i33−3−i3i3i3−i33−3−33−i3i33−3-11-11−ii−ii00000000000000000000
χ542-22-222-2-2-12i−2i2i−2i2-22i−2i2i−2i-221-11-11-11−ii−ii-11-11−ii−ii000002-20002i−2ii3−i3−33i3−i3−i3i3−333−3i3−i3−33-11-11−ii−ii00000000000000000000
χ552-22-222-2-2-12i−2i2i−2i2-22i−2i2i−2i-221-11-11-11−ii−ii-11-11−ii−ii00000-22000−2i2i−i3i33−3i3−i3−i3i3−333−3−i3i33−31-11-1i−ii−i00000000000000000000
χ562-22-222-2-2-12i−2i2i−2i2-22i−2i2i−2i-221-11-11-11−ii−ii-11-11−ii−ii00000-22000−2i2ii3−i3−33−i3i3i3−i33−3−33i3−i3−331-11-1i−ii−i00000000000000000000
χ572-22-222-2-2-12i−2i2i−2i-22−2i2i−2i2i2-21-11-11-11−ii−ii1-11-1i−ii−i002-20002i−2i000−i3i3−33-11-11−ii−iii3−i33−3−i3i3i3−i33−3−3300000000000000000000
χ582-22-222-2-2-12i−2i2i−2i-22−2i2i−2i2i2-21-11-11-11−ii−ii1-11-1i−ii−i002-20002i−2i000i3−i33−3-11-11−ii−ii−i3i3−33i3−i3−i3i3−333−300000000000000000000
χ592-22-222-2-2-12i−2i2i−2i-22−2i2i−2i2i2-21-11-11-11−ii−ii1-11-1i−ii−i00-22000−2i2i000−i3i3−331-11-1i−ii−ii3−i33−3i3−i3−i3i3−333−300000000000000000000
χ602-22-222-2-2-12i−2i2i−2i-22−2i2i−2i2i2-21-11-11-11−ii−ii1-11-1i−ii−i00-22000−2i2i000i3−i33−31-11-1i−ii−i−i3i3−33−i3i3i3−i33−3−3300000000000000000000
χ612-22-222-2-2-1−2i2i−2i2i2-2−2i2i−2i2i-221-11-11-11i−ii−i-11-11i−ii−i000002-2000−2i2i−i3i3−33−i3i3i3−i3−333−3−i3i3−33-11-11i−ii−i00000000000000000000
χ622-22-222-2-2-1−2i2i−2i2i2-2−2i2i−2i2i-221-11-11-11i−ii−i-11-11i−ii−i000002-2000−2i2ii3−i33−3i3−i3−i3i33−3−33i3−i33−3-11-11i−ii−i00000000000000000000
χ632-22-222-2-2-1−2i2i−2i2i2-2−2i2i−2i2i-221-11-11-11i−ii−i-11-11i−ii−i00000-220002i−2i−i3i3−33i3−i3−i3i33−3−33−i3i3−331-11-1−ii−ii00000000000000000000
χ642-22-222-2-2-1−2i2i−2i2i2-2−2i2i−2i2i-221-11-11-11i−ii−i-11-11i−ii−i00000-220002i−2ii3−i33−3−i3i3i3−i3−333−3i3−i33−31-11-1−ii−ii00000000000000000000
χ652-22-222-2-2-1−2i2i−2i2i-222i−2i2i−2i2-21-11-11-11i−ii−i1-11-1−ii−ii002-2000−2i2i000−i3i33−3-11-11i−ii−ii3−i3−33−i3i3i3−i3−333−300000000000000000000
χ662-22-222-2-2-1−2i2i−2i2i-222i−2i2i−2i2-21-11-11-11i−ii−i1-11-1−ii−ii002-2000−2i2i000i3−i3−33-11-11i−ii−i−i3i33−3i3−i3−i3i33−3−3300000000000000000000
χ672-22-222-2-2-1−2i2i−2i2i-222i−2i2i−2i2-21-11-11-11i−ii−i1-11-1−ii−ii00-220002i−2i000−i3i33−31-11-1−ii−iii3−i3−33i3−i3−i3i33−3−3300000000000000000000
χ682-22-222-2-2-1−2i2i−2i2i-222i−2i2i−2i2-21-11-11-11i−ii−i1-11-1−ii−ii00-220002i−2i000i3−i3−331-11-1−ii−ii−i3i33−3−i3i3i3−i3−333−300000000000000000000
χ692-2-222-2-2222-2-22222-2-22-2-2-2-2-2-22222-2-222-2-222-2-220000000000000000000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ702-2-222-2-2222-2-22222-2-22-2-2-2-2-2-22222-2-222-2-222-2-22000000000000000000000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ712-2-222-2-2222-2-22-2-2-222-222-2-2-2-22222-2-22-222-2-222-200000000000000000000000000000000000000000000000000002-22-2
χ722-2-222-2-2222-2-22-2-2-222-222-2-2-2-22222-2-22-222-2-222-20000000000000000000000000000000000000000000000000000-22-22
χ732-2-222-2-222-222-222-222-2-2-2-2-2-2-2222-222-22-2-22-222-20000000000000000000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ742-2-222-2-222-222-222-222-2-2-2-2-2-2-2222-222-22-2-22-222-2000000000000000000000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ752-2-222-2-222-222-2-2-22-2-2222-2-2-2-2222-222-2-222-22-2-2200000000000000000000000000000000000000000000000000002-2-22
χ762-2-222-2-222-222-2-2-22-2-2222-2-2-2-2222-222-2-222-22-2-220000000000000000000000000000000000000000000000000000-222-2
χ774444-4-4-4-440000000000004-4-444-4-400000000000000000000000000000000000000000000000022−2222−220000000000000000
χ784444-4-4-4-440000000000004-4-444-4-4000000000000000000000000000000000000000000000000−2222−22220000000000000000
χ7944-4-44-44-4-24i4i−4i−4i4-44i4i−4i−4i4-4-22-222-22−2i−2i2i2i-2-222−2i−2i2i2i00000000000000000000000000000000000000000000000000000000
χ8044-4-44-44-4-24i4i−4i−4i-44−4i−4i4i4i-44-22-222-22−2i−2i2i2i22-2-22i2i−2i−2i00000000000000000000000000000000000000000000000000000000
χ8144-4-44-44-4-2−4i−4i4i4i4-4−4i−4i4i4i4-4-22-222-222i2i−2i−2i-2-2222i2i−2i−2i00000000000000000000000000000000000000000000000000000000
χ8244-4-44-44-4-2−4i−4i4i4i-444i4i−4i−4i-44-22-222-222i2i−2i−2i22-2-2−2i−2i2i2i00000000000000000000000000000000000000000000000000000000
χ8344-4-4-44-44400000000000044-4-4-4-440000000000000000000000000000000000000000000000000000−2i22i2−2i22i2000000000000
χ8444-4-4-44-44400000000000044-4-4-4-4400000000000000000000000000000000000000000000000000002i2−2i22i2−2i2000000000000
χ854-44-4-4-4444000000000000-4-444-4-44000000000000000000000000000000000000000000000000000022−22−2222000000000000
χ864-44-4-4-4444000000000000-4-444-4-440000000000000000000000000000000000000000000000000000−222222−22000000000000
χ874-4-444-4-44-24-4-44444-4-44-4-42222-2-2-2-222-2-222-2-222-200000000000000000000000000000000000000000000000000000000
χ884-4-444-4-44-24-4-44-4-4-444-4442222-2-2-2-222-22-2-222-2-2200000000000000000000000000000000000000000000000000000000
χ894-4-444-4-44-2-444-444-444-4-4-42222-2-2-22-2-22-222-22-2-2200000000000000000000000000000000000000000000000000000000
χ904-4-444-4-44-2-444-4-4-44-4-44442222-2-2-22-2-222-2-22-222-200000000000000000000000000000000000000000000000000000000
χ914-4-44-444-44000000000000-444-44-4-4000000000000000000000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ924-4-44-444-44000000000000-444-44-4-40000000000000000000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ938888-8-8-8-8-4000000000000-444-4-44400000000000000000000000000000000000000000000000000000000000000000000
χ9488-8-8-88-88-4000000000000-4-44444-400000000000000000000000000000000000000000000000000000000000000000000
χ958-88-8-8-888-400000000000044-4-444-400000000000000000000000000000000000000000000000000000000000000000000
χ968-8-88-888-8-40000000000004-4-44-44400000000000000000000000000000000000000000000000000000000000000000000

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