Finite Group Databasebeta

← Group #10853232

Character table — Group #10853232

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222444444444444448888888888888888888888888881212121212121616161616242424242424242424242448
order122222223444466666664444441212121212121212444448888121212121212121212122424242424242424224444412121212444444488884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-111111-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111
χ51111111111111111111111-1-1-1-1111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-11-1-111-1-1-1-11
χ61111111111111111111111-1-1-1-1111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-111-1-11111-1
χ71111111111111111111111-1-1-1-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-11-1-1-1-11111-1
χ81111111111111111111111-1-1-1-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-111-11111-1-1-1-11
χ911111111111111111111-1-11111111-1-1-1-11-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-11111-1-1-111-1-111-1
χ1011111111111111111111-1-11111111-1-1-1-11-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-111-1-1111-1-111-1-11
χ1111111111111111111111-1-11111111-1-1-1-11-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1111-1-111-1-1-1-1-111-1-11
χ1211111111111111111111-1-11111111-1-1-1-11-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-1-111111-1-111-1
χ1311111111111111111111-1-1-1-1-1-1111-1-1-1-11-11111-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-111-1-1-1111111-1-1-1
χ1411111111111111111111-1-1-1-1-1-1111-1-1-1-11-11111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-111111-1-1-1-1-1-1111
χ1511111111111111111111-1-1-1-1-1-1111-1-1-1-11-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1111-1-1-1-1-111-1-1-1-1111
χ1611111111111111111111-1-1-1-1-1-1111-1-1-1-11-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-1111-1-11111-1-1-1
χ17222222222-2-2-2-22222222220000-2-2-22222-2-200000000-2-2000000000000000022-2-2-2-200000002000000000
χ18222222222-2-2-2-22222222220000-2-2-22222-2-200000000-2-20000000000000000-2-222220000000-2000000000
χ19222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-220000000022000000000000000022-2-2220000000-2000000000
χ20222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-2200000000220000000000000000-2-222-2-200000002000000000
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
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-12-2-222-2-2-2-2-1-111111111111111110000002-1-1-1-1000000000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-12-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-1000000-21111000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-22222-1-1-11111-1-2-2-22222-2-211-1-1-1-11111-1-1-1-11111000000-211-1-1000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-22222-1-1-11111-1-2-2-2-2-2-2-22211-1-1-1-111111111-1-1-1-10000002-1-111000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-11111-1-22222-2-222111111-1-1-1-11111-1-1-1-1000000-211-1-1000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-11111-1-222-2-222-2-2111111-1-1-1-1-1-1-1-111110000002-1-111000000000000
χ2922-22-2-22-222-2-22-2222-2-2-2002i2i−2i−2i2-2-2000020002i−2i2-200002i2i−2i−2i000022-2-200000000000002i−2i000000000000
χ3022-22-2-22-222-2-22-2222-2-2-2002i2i−2i−2i2-2-200002000−2i2i-2200002i2i−2i−2i0000-2-2220000000000000−2i2i000000000000
χ3122-22-2-22-222-2-22-2222-2-2-200−2i−2i2i2i2-2-2000020002i−2i-220000−2i−2i2i2i0000-2-22200000000000002i−2i000000000000
χ3222-22-2-22-222-2-22-2222-2-2-200−2i−2i2i2i2-2-200002000−2i2i2-20000−2i−2i2i2i000022-2-20000000000000−2i2i000000000000
χ3322-22-2-22-2-12-2-221-1-1-1111002i2i−2i−2i-111−i3−i3i3i3-10002i−2i2-200−i3i3−i−iii33−3−3-1-111−i3−i3i3i300000003−3−ii000000000000
χ3422-22-2-22-2-12-2-221-1-1-1111002i2i−2i−2i-111−i3−i3i3i3-1000−2i2i-2200−i3i3−i−iii33−3−311-1-1i3i3−i3−i30000000−33i−i000000000000
χ3522-22-2-22-2-12-2-221-1-1-1111002i2i−2i−2i-111i3i3−i3−i3-10002i−2i2-200i3−i3−i−iii−3−333-1-111i3i3−i3−i30000000−33−ii000000000000
χ3622-22-2-22-2-12-2-221-1-1-1111002i2i−2i−2i-111i3i3−i3−i3-1000−2i2i-2200i3−i3−i−iii−3−33311-1-1−i3−i3i3i300000003−3i−i000000000000
χ3722-22-2-22-2-12-2-221-1-1-111100−2i−2i2i2i-111−i3−i3i3i3-10002i−2i-2200−i3i3ii−i−i−3−33311-1-1i3i3−i3−i300000003−3−ii000000000000
χ3822-22-2-22-2-12-2-221-1-1-111100−2i−2i2i2i-111−i3−i3i3i3-1000−2i2i2-200−i3i3ii−i−i−3−333-1-111−i3−i3i3i30000000−33i−i000000000000
χ3922-22-2-22-2-12-2-221-1-1-111100−2i−2i2i2i-111i3i3−i3−i3-10002i−2i-2200i3−i3ii−i−i33−3−311-1-1−i3−i3i3i30000000−33−ii000000000000
χ4022-22-2-22-2-12-2-221-1-1-111100−2i−2i2i2i-111i3i3−i3−i3-1000−2i2i2-200i3−i3ii−i−i33−3−3-1-111i3i3−i3−i300000003−3i−i000000000000
χ412-222-22-2-2222-2-222-2-22-2-2002-22-222-20000-2000000000002-22-20000000000002-22-200000002-20000000000
χ422-222-22-2-2222-2-222-2-22-2-2002-22-222-20000-2000000000002-22-2000000000000-22-220000000-220000000000
χ432-222-22-2-2222-2-222-2-22-2-200-22-2222-20000-200000000000-22-220000000000002-22-20000000-220000000000
χ442-222-22-2-2222-2-222-2-22-2-200-22-2222-20000-200000000000-22-22000000000000-22-2200000002-20000000000
χ452-222-22-2-22-2-22222-2-22-2-2000000-2-220000202i−2i0000000000002i−2i2i−2i000000002-2-2200000000002i−2i0000000
χ462-222-22-2-22-2-22222-2-22-2-2000000-2-220000202i−2i0000000000002i−2i2i−2i00000000-222-20000000000−2i2i0000000
χ472-222-22-2-22-2-22222-2-22-2-2000000-2-22000020−2i2i000000000000−2i2i−2i2i000000002-2-220000000000−2i2i0000000
χ482-222-22-2-22-2-22222-2-22-2-2000000-2-22000020−2i2i000000000000−2i2i−2i2i00000000-222-200000000002i−2i0000000
χ492-2-222-2-2222-22-2-22-2-2-222002i−2i−2i2i2-220000-2000000000002i−2i−2i2i00000000000000000000000000002-2002i−2i0
χ502-2-222-2-2222-22-2-22-2-2-222002i−2i−2i2i2-220000-2000000000002i−2i−2i2i0000000000000000000000000000-2200−2i2i0
χ512-2-222-2-2222-22-2-22-2-2-22200−2i2i2i−2i2-220000-200000000000−2i2i2i−2i00000000000000000000000000002-200−2i2i0
χ522-2-222-2-2222-22-2-22-2-2-22200−2i2i2i−2i2-220000-200000000000−2i2i2i−2i0000000000000000000000000000-22002i−2i0
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-2440000222-2-2-2-22-40000000022000000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-4000022222222400000000-2-2000000000000000000000000000000000000000
χ55444-4-4-4-4440000-4-44-44-440000000000000000000000000000000000000000000004i−4i00000000000000000
χ56444-4-4-4-4440000-4-44-44-44000000000000000000000000000000000000000000000−4i4i00000000000000000
χ5744-44-4-44-44-444-4-4444-4-4-4000000-4440000-400000000000000000000000000000000000000000000000000
χ5844-44-4-44-4-2-444-42-2-2-22220000002-2-2−2i3−2i32i32i320000000002i3−2i3000000000000000000000000000000000000000
χ5944-44-4-44-4-2-444-42-2-2-22220000002-2-22i32i3−2i3−2i32000000000−2i32i3000000000000000000000000000000000000000
χ6044-4-444-4-4400004-44-4-44-40000000000000000000000000000000000000000000000000000000000022−22000
χ6144-4-444-4-4400004-44-4-44-400000000000000000000000000000000000000000000000000000000000−2222000
χ624-444-44-4-4-244-4-4-2-222-222004-44-4-2-220000200000000000-22-2200000000000000000000000000000000000
χ634-444-44-4-4-244-4-4-2-222-22200-44-44-2-2200002000000000002-22-200000000000000000000000000000000000
χ644-444-44-4-4-2-4-444-2-222-22200000022-20000-204i−4i000000000000−2i2i−2i2i0000000000000000000000000000000
χ654-444-44-4-4-2-4-444-2-222-22200000022-20000-20−4i4i0000000000002i−2i2i−2i0000000000000000000000000000000
χ664-44-44-44-440000-4-4-4444-44i−4i00000004i−4i4i−4i000000000000000000000000000000000000000000000000000
χ674-44-44-44-440000-4-4-4444-4−4i4i0000000−4i4i−4i4i000000000000000000000000000000000000000000000000000
χ684-44-44-44-4-20000222-2-2-224i−4i0000000−2i2i−2i2i000000000000000000006−66−6i6−i6i6−i600000000000000000000000
χ694-44-44-44-4-20000222-2-2-224i−4i0000000−2i2i−2i2i00000000000000000000−66−66−i6i6−i6i600000000000000000000000
χ704-44-44-44-4-20000222-2-2-22−4i4i00000002i−2i2i−2i000000000000000000006−66−6−i6i6−i6i600000000000000000000000
χ714-44-44-44-4-20000222-2-2-22−4i4i00000002i−2i2i−2i00000000000000000000−66−66i6−i6i6−i600000000000000000000000
χ724-4-444-4-444-44-44-44-4-4-444000000-44-40000400000000000000000000000000000000000000000000000000
χ734-4-444-4-44-24-44-42-2222-2-2004i−4i−4i4i-22-20000200000000000−2i2i2i−2i00000000000000000000000000000000000
χ744-4-444-4-44-24-44-42-2222-2-200−4i4i4i−4i-22-200002000000000002i−2i−2i2i00000000000000000000000000000000000
χ754-4-444-4-44-2-44-442-2222-2-20000002-220000-2000000000000000−2i32i32i3−2i30000000000000000000000000000000
χ764-4-444-4-44-2-44-442-2222-2-20000002-220000-20000000000000002i3−2i3−2i32i30000000000000000000000000000000
χ774-4-4-4-4444400004-4-44-4-4400000000000000000000022−220000000000000022−22−222200000000000000000000000
χ784-4-4-4-4444400004-4-44-4-44000000000000000000000−222200000000000000−222222−2200000000000000000000000
χ794-4-4-4-4444-20000-222-222-200000000023−23−23230000000022−220000000000−666−6−222−200000000000000000000000
χ804-4-4-4-4444-20000-222-222-200000000023−23−232300000000−222200000000006−6−662−2−2200000000000000000000000
χ814-4-4-4-4444-20000-222-222-2000000000−232323−230000000022−2200000000006−6−66−222−200000000000000000000000
χ824-4-4-4-4444-20000-222-222-2000000000−232323−2300000000−22220000000000−666−62−2−2200000000000000000000000
χ83888-8-8-8-88-4000044-44-44-40000000000000000000000000000000000000000000000000000000000000000
χ8488-8-888-8-8-40000-44-444-440000000000000000000000000000000000000000000000000000000000000000

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