Finite Group Databasebeta

← Group #10855126

Character table — Group #10855126

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222444444444444448888888888888888888888888881212121212121616161616242424242424242424242448
order122222223444466666664444441212121212121212444448888121212121212121212122424242424242424224444412121212244444488884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-11-1-11111-1-1-1-1-1
χ41111111111111111111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111
χ51111111111111111111111-1-1-1-111111111-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11
χ61111111111111111111111-1-1-1-111111111-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-111111111-1
χ71111111111111111111111-1-1-1-111111111-1-11-1-1111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-11-1-1-1-1-1-11111-1
χ81111111111111111111111-1-1-1-111111111-1-11-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11
χ911111111111111111111-1-11111-1-1-1-11111-1-1-111-1-111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-111-11111-1-1-1-111-1
χ1011111111111111111111-1-11111-1-1-1-11111-1-1-111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1111-1-1-1-11111-1-11
χ1111111111111111111111-1-11111-1-1-1-11111-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1111-1-1-1-1-111-1-111-1-11
χ1211111111111111111111-1-11111-1-1-1-11111-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111-1-1111-1-111-1-111-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1111111-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-111-111-1-11111-1-1-1
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1111111-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1111-1-111-1-1-1-1111
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1111-1-1-1-1-1-1-111-1-1111
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111-1-111111-1-111-1-1-1
χ17222222222-2-2-2-222222222200002222-2-2-2-200-2000000-2-2000000000000000022-2-2-2-200000200000000000
χ18222222222-2-2-2-222222222200002222-2-2-2-200-2000000-2-20000000000000000-2-2222200000-200000000000
χ19222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-200200000022000000000000000022-2-22200000-200000000000
χ20222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-2002000000220000000000000000-2-222-2-200000200000000000
χ2122222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000002-1-1-1-1000000000000
χ2222222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1222-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111000000-21111000000000000
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-2-2222-2-2-2-2-1-111111111111111110000002-1-1-1-1000000000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-2-22-2-22222-1-111111111-1-1-1-1-1-1-1-1000000-21111000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-222221111-1-1-1-1-2-2-222-2-222111111-1-1-1-1-1-1-1-11111000000-211-1-1000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-222221111-1-1-1-1-2-2-2-2-222-2-2111111-1-1-1-11111-1-1-1-10000002-1-111000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-1-122-22222-2-211-1-1-1-111111111-1-1-1-1000000-211-1-1000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-1-122-2-2-2-2-22211-1-1-1-11111-1-1-1-111110000002-1-111000000000000
χ2922-22-22-2-22-2-2222-2-2-222-2002i2i−2i−2i00002-22-20002i−2i002-20000002i2i−2i−2i22-2-200000000000002i−2i000000000000
χ3022-22-22-2-22-2-2222-2-2-222-2002i2i−2i−2i00002-22-2000−2i2i00-220000002i2i−2i−2i-2-2220000000000000−2i2i000000000000
χ3122-22-22-2-22-2-2222-2-2-222-200−2i−2i2i2i00002-22-20002i−2i00-22000000−2i−2i2i2i-2-22200000000000002i−2i000000000000
χ3222-22-22-2-22-2-2222-2-2-222-200−2i−2i2i2i00002-22-2000−2i2i002-2000000−2i−2i2i2i22-2-20000000000000−2i2i000000000000
χ3322-22-22-2-2-1-2-222-1111-1-11002i2i−2i−2i33−3−3-11-110002i−2i002-23−3−i3−i3i3i3−i−iii-1-11133−3−30000000−i3i3−ii000000000000
χ3422-22-22-2-2-1-2-222-1111-1-11002i2i−2i−2i33−3−3-11-11000−2i2i00-223−3−i3−i3i3i3−i−iii11-1-1−3−3330000000i3−i3i−i000000000000
χ3522-22-22-2-2-1-2-222-1111-1-11002i2i−2i−2i−3−333-11-110002i−2i002-2−33i3i3−i3−i3−i−iii-1-111−3−3330000000i3−i3−ii000000000000
χ3622-22-22-2-2-1-2-222-1111-1-11002i2i−2i−2i−3−333-11-11000−2i2i00-22−33i3i3−i3−i3−i−iii11-1-133−3−30000000−i3i3i−i000000000000
χ3722-22-22-2-2-1-2-222-1111-1-1100−2i−2i2i2i33−3−3-11-110002i−2i00-223−3i3i3−i3−i3ii−i−i11-1-1−3−3330000000−i3i3−ii000000000000
χ3822-22-22-2-2-1-2-222-1111-1-1100−2i−2i2i2i33−3−3-11-11000−2i2i002-23−3i3i3−i3−i3ii−i−i-1-11133−3−30000000i3−i3i−i000000000000
χ3922-22-22-2-2-1-2-222-1111-1-1100−2i−2i2i2i−3−333-11-110002i−2i00-22−33−i3−i3i3i3ii−i−i11-1-133−3−30000000i3−i3−ii000000000000
χ4022-22-22-2-2-1-2-222-1111-1-1100−2i−2i2i2i−3−333-11-11000−2i2i002-2−33−i3−i3i3i3ii−i−i-1-111−3−3330000000−i3i3i−i000000000000
χ412-22-222-2-222-2-22-2-222-22-2002i−2i2i−2i0000-222-20000000000000002i−2i2i−2i000000002-22-200000000002i−2i0000000
χ422-22-222-2-222-2-22-2-222-22-2002i−2i2i−2i0000-222-20000000000000002i−2i2i−2i00000000-22-220000000000−2i2i0000000
χ432-22-222-2-222-2-22-2-222-22-200−2i2i−2i2i0000-222-2000000000000000−2i2i−2i2i000000002-22-20000000000−2i2i0000000
χ442-22-222-2-222-2-22-2-222-22-200−2i2i−2i2i0000-222-2000000000000000−2i2i−2i2i00000000-22-2200000000002i−2i0000000
χ452-22-222-2-22-222-2-2-222-22-200000000002-2-222i−2i0000000002i−2i2i−2i0000000000002-2-220000000000002i−2i00000
χ462-22-222-2-22-222-2-2-222-22-200000000002-2-222i−2i0000000002i−2i2i−2i000000000000-222-2000000000000−2i2i00000
χ472-22-222-2-22-222-2-2-222-22-200000000002-2-22−2i2i000000000−2i2i−2i2i0000000000002-2-22000000000000−2i2i00000
χ482-22-222-2-22-222-2-2-222-22-200000000002-2-22−2i2i000000000−2i2i−2i2i000000000000-222-20000000000002i−2i00000
χ492-2-2-2-22222-22-22-22-2-2-222002-2-220000-2-2220000000000000002-2-22000000000000000000002-20000002-20
χ502-2-2-2-22222-22-22-22-2-2-222002-2-220000-2-2220000000000000002-2-2200000000000000000000-22000000-220
χ512-2-2-2-22222-22-22-22-2-2-22200-222-20000-2-222000000000000000-222-2000000000000000000002-2000000-220
χ522-2-2-2-22222-22-22-22-2-2-22200-222-20000-2-222000000000000000-222-200000000000000000000-220000002-20
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-2440000-2-2-2-2222200-400000022000000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-4000022222222004000000-2-2000000000000000000000000000000000000000
χ55444-4-4-4-4440000444-4-4-4-44-400004-44-4000000000000000000000000000000000000000000000000000000
χ56444-4-4-4-4440000444-4-4-4-4-440000-44-44000000000000000000000000000000000000000000000000000000
χ57444-4-4-4-44-20000-2-2-222224-40000-22-2200000000000000000000000i6−i6i6−i6i6−i6i6−i600000000000000000000000
χ58444-4-4-4-44-20000-2-2-222224-40000-22-2200000000000000000000000−i6i6−i6i6−i6i6−i6i600000000000000000000000
χ59444-4-4-4-44-20000-2-2-22222-4400002-22-200000000000000000000000i6−i6i6−i6−i6i6−i6i600000000000000000000000
χ60444-4-4-4-44-20000-2-2-22222-4400002-22-200000000000000000000000−i6i6−i6i6i6−i6i6−i600000000000000000000000
χ6144-44-44-4-4444-4-44-4-4-444-40000000000-44-4400000000000000000000000000000000000000000000000000
χ6244-44-44-4-4-244-4-4-2222-2-220000002323−23−232-22-2000000000−2323000000000000000000000000000000000000000
χ6344-44-44-4-4-244-4-4-2222-2-22000000−23−2323232-22-200000000023−23000000000000000000000000000000000000000
χ6444-4-44-44-4400004-4-44-4-440000000000000000000−2i22i20000000000000000−2i22i22i2−2i200000000000000000000000
χ6544-4-44-44-4400004-4-44-4-4400000000000000000002i2−2i200000000000000002i2−2i2−2i22i200000000000000000000000
χ6644-4-44-44-4-20000-222-222-200000023−23−2323000000000−2i22i2000000000000i6−i6−i6i6i2−i2−i2i200000000000000000000000
χ6744-4-44-44-4-20000-222-222-200000023−23−23230000000002i2−2i2000000000000−i6i6i6−i6−i2i2i2−i200000000000000000000000
χ6844-4-44-44-4-20000-222-222-2000000−232323−23000000000−2i22i2000000000000−i6i6i6−i6i2−i2−i2i200000000000000000000000
χ6944-4-44-44-4-20000-222-222-2000000−232323−230000000002i2−2i2000000000000i6−i6−i6i6−i2i2i2−i200000000000000000000000
χ704-444-4-44-440000-4-44-44-440000000000000000000000000000000000000000000004i−4i00000000000000000
χ714-444-4-44-440000-4-44-44-44000000000000000000000000000000000000000000000−4i4i00000000000000000
χ724-44-444-4-4-24-4-4422-2-22-22004i−4i4i−4i00002-2-22000000000000000−2i2i−2i2i0000000000000000000000000000000
χ734-44-444-4-4-24-4-4422-2-22-2200−4i4i−4i4i00002-2-220000000000000002i−2i2i−2i0000000000000000000000000000000
χ744-44-444-4-4-2-444-422-2-22-220000000000-222-24i−4i000000000−2i2i−2i2i00000000000000000000000000000000000
χ754-44-444-4-4-2-444-422-2-22-220000000000-222-2−4i4i0000000002i−2i2i−2i00000000000000000000000000000000000
χ764-4-444-4-4440000-44-444-4-400000000000000000000000000000000000000000000000000000000000−2i22i2000
χ774-4-444-4-4440000-44-444-4-4000000000000000000000000000000000000000000000000000000000002i2−2i2000
χ784-4-4-4-444444-44-4-44-4-4-444000000000044-4-400000000000000000000000000000000000000000000000000
χ794-4-4-4-4444-24-44-42-2222-2-20000000000-2-2220000000000023−23−232300000000000000000000000000000000000
χ804-4-4-4-4444-24-44-42-2222-2-20000000000-2-22200000000000−232323−2300000000000000000000000000000000000
χ814-4-4-4-4444-2-44-442-2222-2-2004-4-44000022-2-2000000000000000-222-20000000000000000000000000000000
χ824-4-4-4-4444-2-44-442-2222-2-200-444-4000022-2-20000000000000002-2-220000000000000000000000000000000
χ838-888-8-88-8-4000044-44-44-40000000000000000000000000000000000000000000000000000000000000000
χ848-8-888-8-88-400004-44-4-4440000000000000000000000000000000000000000000000000000000000000000

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