Finite Group Databasebeta

← Group #10855066

Character table — Group #10855066

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
χ31111111111111111111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-111111-1-1-1-1-1-1-1
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
χ51111111111111111111111-1-1-1-111111111-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-11
χ61111111111111111111111-1-1-1-111111111-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-11111-1-11111-1
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
χ911111111111111111111-1-11111-1-1-1-11111-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-111-1-1-111-1-111-1-111-1
χ1011111111111111111111-1-11111-1-1-1-11111-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-111-1-11-1-111-1-111-1-11
χ1111111111111111111111-1-11111-1-1-1-11111-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-11-1-111-111-1-1-1-111-1-11
χ1211111111111111111111-1-11111-1-1-1-11111-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111-1-1111-1-11111-1-111-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1111111-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-111-1-1-1-1-1111111-1-1-1
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1111111-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-111-1-1111-1-1-1-1-1-1111
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-11111-1-11-1-111-1-1-111-1-1-1-1111
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111-1-111111-1-11111-1-1-1
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
χ2522222222-12222-1-1-1-1-1-1-1-2-222221111-1-1-1-1-2-2-222-2-22211-1-1-1-11111-1-1-1-11111000000-2-1-111000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-222221111-1-1-1-1-2-2-2-2-222-2-211-1-1-1-111111111-1-1-1-1000000211-1-1000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-1-122-22222-2-2111111-1-1-1-11111-1-1-1-1000000-2-1-111000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-1-122-2-2-2-2-222111111-1-1-1-1-1-1-1-11111000000211-1-1000000000000
χ2922-22-2-22-22-2-2222-2-22-2-22002i2i−2i−2i00002-22-20002i−2i002-2002i2i−2i−2i000022-2-2000000000002i−2i00000000000000
χ3022-22-2-22-22-2-2222-2-22-2-22002i2i−2i−2i00002-22-2000−2i2i00-22002i2i−2i−2i0000-2-22200000000000−2i2i00000000000000
χ3122-22-2-22-22-2-2222-2-22-2-2200−2i−2i2i2i00002-22-20002i−2i00-2200−2i−2i2i2i0000-2-222000000000002i−2i00000000000000
χ3222-22-2-22-22-2-2222-2-22-2-2200−2i−2i2i2i00002-22-2000−2i2i002-200−2i−2i2i2i000022-2-200000000000−2i2i00000000000000
χ3322-22-2-22-2-1-2-222-111-111-1002i2i−2i−2i33−3−3-11-110002i−2i002-23−3−i−iii−i3−i3i3i3-1-11133−3−30000000−ii−i3i3000000000000
χ3422-22-2-22-2-1-2-222-111-111-1002i2i−2i−2i33−3−3-11-11000−2i2i00-223−3−i−iii−i3−i3i3i311-1-1−3−3330000000i−ii3−i3000000000000
χ3522-22-2-22-2-1-2-222-111-111-1002i2i−2i−2i−3−333-11-110002i−2i002-2−33−i−iiii3i3−i3−i3-1-111−3−3330000000−iii3−i3000000000000
χ3622-22-2-22-2-1-2-222-111-111-1002i2i−2i−2i−3−333-11-11000−2i2i00-22−33−i−iiii3i3−i3−i311-1-133−3−30000000i−i−i3i3000000000000
χ3722-22-2-22-2-1-2-222-111-111-100−2i−2i2i2i33−3−3-11-110002i−2i00-223−3ii−i−ii3i3−i3−i311-1-1−3−3330000000−ii−i3i3000000000000
χ3822-22-2-22-2-1-2-222-111-111-100−2i−2i2i2i33−3−3-11-11000−2i2i002-23−3ii−i−ii3i3−i3−i3-1-11133−3−30000000i−ii3−i3000000000000
χ3922-22-2-22-2-1-2-222-111-111-100−2i−2i2i2i−3−333-11-110002i−2i00-22−33ii−i−i−i3−i3i3i311-1-133−3−30000000−iii3−i3000000000000
χ4022-22-2-22-2-1-2-222-111-111-100−2i−2i2i2i−3−333-11-11000−2i2i002-2−33ii−i−i−i3−i3i3i3-1-111−3−3330000000i−i−i3i3000000000000
χ412-22-2-222-222-2-22-222-2-2-22002i−2i2i−2i0000-222-2000000000002i−2i2i−2i0000000000002-22-2000000002i−2i000000000
χ422-22-2-222-222-2-22-222-2-2-22002i−2i2i−2i0000-222-2000000000002i−2i2i−2i000000000000-22-2200000000−2i2i000000000
χ432-22-2-222-222-2-22-222-2-2-2200−2i2i−2i2i0000-222-200000000000−2i2i−2i2i0000000000002-22-200000000−2i2i000000000
χ442-22-2-222-222-2-22-222-2-2-2200−2i2i−2i2i0000-222-200000000000−2i2i−2i2i000000000000-22-22000000002i−2i000000000
χ452-22-2-222-22-222-2-222-2-2-2200000000002-2-222i−2i00000000000002i−2i2i−2i000000002-2-2200000000002i−2i0000000
χ462-22-2-222-22-222-2-222-2-2-2200000000002-2-222i−2i00000000000002i−2i2i−2i00000000-222-20000000000−2i2i0000000
χ472-22-2-222-22-222-2-222-2-2-2200000000002-2-22−2i2i0000000000000−2i2i−2i2i000000002-2-220000000000−2i2i0000000
χ482-22-2-222-22-222-2-222-2-2-2200000000002-2-22−2i2i0000000000000−2i2i−2i2i00000000-222-200000000002i−2i0000000
χ492-2-2-22-2222-22-22-2-2-2-2222002-2-220000-2-222000000000002-2-2200000000000000000000000000002-2002-20
χ502-2-2-22-2222-22-22-2-2-2-2222002-2-220000-2-222000000000002-2-220000000000000000000000000000-2200-220
χ512-2-2-22-2222-22-22-2-2-2-222200-222-20000-2-22200000000000-222-200000000000000000000000000002-200-220
χ522-2-2-22-2222-22-22-2-2-2-222200-222-20000-2-22200000000000-222-20000000000000000000000000000-22002-20
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
χ55444-4-4-4-444000044-4-44-4-40000000000000000000000000000000000000000000004i−4i00000000000000000
χ56444-4-4-4-444000044-4-44-4-4000000000000000000000000000000000000000000000−4i4i00000000000000000
χ5744-44-4-44-4444-4-44-4-44-4-440000000000-44-4400000000000000000000000000000000000000000000000000
χ5844-44-4-44-4-244-4-4-222-222-20000002323−23−232-22-2000000000−2323000000000000000000000000000000000000000
χ5944-44-4-44-4-244-4-4-222-222-2000000−23−2323232-22-200000000023−23000000000000000000000000000000000000000
χ6044-4-444-4-4400004-44-4-44-40000000000000000000000000000000000000000000000000000000000022−22000
χ6144-4-444-4-4400004-44-4-44-400000000000000000000000000000000000000000000000000000000000−2222000
χ624-4444-4-4-440000-44-44-44-44-400004-44-4000000000000000000000000000000000000000000000000000000
χ634-4444-4-4-440000-44-44-44-4-440000-44-44000000000000000000000000000000000000000000000000000000
χ644-4444-4-4-4-200002-22-22-224-40000-22-22000000000000000000000006−66−66−66−600000000000000000000000
χ654-4444-4-4-4-200002-22-22-224-40000-22-2200000000000000000000000−66−66−66−6600000000000000000000000
χ664-4444-4-4-4-200002-22-22-22-4400002-22-2000000000000000000000006−66−6−66−6600000000000000000000000
χ674-4444-4-4-4-200002-22-22-22-4400002-22-200000000000000000000000−66−666−66−600000000000000000000000
χ684-44-4-444-4-24-4-442-2-2222-2004i−4i4i−4i00002-2-2200000000000−2i2i−2i2i00000000000000000000000000000000000
χ694-44-4-444-4-24-4-442-2-2222-200−4i4i−4i4i00002-2-22000000000002i−2i2i−2i00000000000000000000000000000000000
χ704-44-4-444-4-2-444-42-2-2222-20000000000-222-24i−4i0000000000000−2i2i−2i2i0000000000000000000000000000000
χ714-44-4-444-4-2-444-42-2-2222-20000000000-222-2−4i4i00000000000002i−2i2i−2i0000000000000000000000000000000
χ724-4-44-44-4440000-4-4444-4-4000000000000000000022−22000000000000000022−22−222200000000000000000000000
χ734-4-44-44-4440000-4-4444-4-40000000000000000000−22220000000000000000−222222−2200000000000000000000000
χ744-4-44-44-44-2000022-2-2-22200000023−23−232300000000022−22000000000000−666−6−222−200000000000000000000000
χ754-4-44-44-44-2000022-2-2-22200000023−23−2323000000000−22220000000000006−6−662−2−2200000000000000000000000
χ764-4-44-44-44-2000022-2-2-222000000−232323−2300000000022−220000000000006−6−66−222−200000000000000000000000
χ774-4-44-44-44-2000022-2-2-222000000−232323−23000000000−2222000000000000−666−62−2−2200000000000000000000000
χ784-4-4-44-44444-44-4-4-4-4-4444000000000044-4-400000000000000000000000000000000000000000000000000
χ794-4-4-44-444-24-44-42222-2-2-20000000000-2-22200000000000000023−23−23230000000000000000000000000000000
χ804-4-4-44-444-24-44-42222-2-2-20000000000-2-222000000000000000−232323−230000000000000000000000000000000
χ814-4-4-44-444-2-44-442222-2-2-2004-4-44000022-2-200000000000-222-200000000000000000000000000000000000
χ824-4-4-44-444-2-44-442222-2-2-200-444-4000022-2-2000000000002-2-2200000000000000000000000000000000000
χ83888-8-8-8-88-40000-4-444-4440000000000000000000000000000000000000000000000000000000000000000
χ8488-8-888-8-8-40000-44-444-440000000000000000000000000000000000000000000000000000000000000000

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