Finite Group Databasebeta

← Group #10845265

Character table — Group #10845265

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222444444444444448888888888888888888888888881212121212121616161616242424242424242424242448
order122222223444466666664444441212121212121212444448888121212121212121212122424242424242424444444412121212224444488884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-11-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-111111-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-11-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111
χ51111111111111111111111-1-1-1-111111111-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-11-1-111-1-1-1-11
χ61111111111111111111111-1-1-1-111111111-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-111-1-11111-1
χ71111111111111111111111-1-1-1-111111111-1-1-1-11111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-11-1-1-1-11111-1
χ81111111111111111111111-1-1-1-111111111-1-1-1-11111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-111-11111-1-1-1-11
χ911111111111111111111-1-11111-1-1-1-11111-1-111-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1-111-1-1-1111111-1-1-1
χ1011111111111111111111-1-11111-1-1-1-11111-1-111-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-111111-1-1-1-1-1-1111
χ1111111111111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-111111-1-1-1-1-111-1-1-1-1111
χ1211111111111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1111-1-1111-1-11111-1-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-11111-1-1-111-1-111-1
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-111-1-1111-1-111-1-11
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111111-1-111-1-1-1-1-111-1-11
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1111-1-1-1-111111-1-111-1
χ17222222222-2-2-2-222222222200002222-2-2-2-20000-20000-2-2000000000000000022-2-2-2-200000002000000000
χ18222222222-2-2-2-222222222200002222-2-2-2-20000-20000-2-20000000000000000-2-222220000000-2000000000
χ19222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-20000200002200000000000000002222-2-20000000-2000000000
χ20222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-2000020000220000000000000000-2-2-2-22200000002000000000
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
χ2222222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-122-2-22-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111000000-21111000000000000
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
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-2-2-2-222222-1-111111111-1-1-1-1-1-1-1-1000000-21111000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-222221111-1-1-1-1-2-222-222-2-211-1-1-1-11111-1-1-1-11111000000-211-1-1000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-222221111-1-1-1-1-2-2-2-2-2-2-22211-1-1-1-111111111-1-1-1-10000002-1-111000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-1-12222-2-2-222111111-1-1-1-11111-1-1-1-1000000-211-1-1000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-1-122-2-2-222-2-2111111-1-1-1-1-1-1-1-111110000002-1-111000000000000
χ2922-2-222-2-222-2-2222-2-2-2-22002i2i−2i−2i00002-22-2002-202i−2i00002i2i−2i−2i00002i2i−2i−2i00000000000002-2000000000000
χ3022-2-222-2-222-2-2222-2-2-2-22002i2i−2i−2i00002-22-200-220−2i2i00002i2i−2i−2i0000−2i−2i2i2i0000000000000-22000000000000
χ3122-2-222-2-222-2-2222-2-2-2-2200−2i−2i2i2i00002-22-2002-20−2i2i0000−2i−2i2i2i0000−2i−2i2i2i00000000000002-2000000000000
χ3222-2-222-2-222-2-2222-2-2-2-2200−2i−2i2i2i00002-22-200-2202i−2i0000−2i−2i2i2i00002i2i−2i−2i0000000000000-22000000000000
χ3322-2-222-2-2-12-2-22-1-11111-1002i2i−2i−2i33−3−3-11-11002-202i−2i003−3−i−iii−i3−i3i3i3−i−iii−i3−i3i3i300000003−3-11000000000000
χ3422-2-222-2-2-12-2-22-1-11111-1002i2i−2i−2i33−3−3-11-1100-220−2i2i003−3−i−iii−i3−i3i3i3ii−i−ii3i3−i3−i30000000−331-1000000000000
χ3522-2-222-2-2-12-2-22-1-11111-1002i2i−2i−2i−3−333-11-11002-202i−2i00−33−i−iiii3i3−i3−i3−i−iiii3i3−i3−i30000000−33-11000000000000
χ3622-2-222-2-2-12-2-22-1-11111-1002i2i−2i−2i−3−333-11-1100-220−2i2i00−33−i−iiii3i3−i3−i3ii−i−i−i3−i3i3i300000003−31-1000000000000
χ3722-2-222-2-2-12-2-22-1-11111-100−2i−2i2i2i33−3−3-11-11002-20−2i2i003−3ii−i−ii3i3−i3−i3ii−i−ii3i3−i3−i300000003−3-11000000000000
χ3822-2-222-2-2-12-2-22-1-11111-100−2i−2i2i2i33−3−3-11-1100-2202i−2i003−3ii−i−ii3i3−i3−i3−i−iii−i3−i3i3i30000000−331-1000000000000
χ3922-2-222-2-2-12-2-22-1-11111-100−2i−2i2i2i−3−333-11-11002-20−2i2i00−33ii−i−i−i3−i3i3i3ii−i−i−i3−i3i3i30000000−33-11000000000000
χ4022-2-222-2-2-12-2-22-1-11111-100−2i−2i2i2i−3−333-11-1100-2202i−2i00−33ii−i−i−i3−i3i3i3−i−iiii3i3−i3−i300000003−31-1000000000000
χ412-22-22-2-22222-2-2-2-22-22-22002i−2i2i−2i000022-2-2000000000002i−2i2i−2i0000000000002-2002-2000000002i−2i0000000
χ422-22-22-2-22222-2-2-2-22-22-22002i−2i2i−2i000022-2-2000000000002i−2i2i−2i000000000000-2200-2200000000−2i2i0000000
χ432-22-22-2-22222-2-2-2-22-22-2200−2i2i−2i2i000022-2-200000000000−2i2i−2i2i0000000000002-2002-200000000−2i2i0000000
χ442-22-22-2-22222-2-2-2-22-22-2200−2i2i−2i2i000022-2-200000000000−2i2i−2i2i000000000000-2200-22000000002i−2i0000000
χ452-22-22-2-222-2-222-2-22-22-220000000000-2-2222-200000000000002-22-2000000002-200-22000002-20000000000
χ462-22-22-2-222-2-222-2-22-22-220000000000-2-2222-200000000000002-22-200000000-22002-200000-220000000000
χ472-22-22-2-222-2-222-2-22-22-220000000000-2-222-220000000000000-22-22000000002-200-2200000-220000000000
χ482-22-22-2-222-2-222-2-22-22-220000000000-2-222-220000000000000-22-2200000000-22002-2000002-20000000000
χ492-2-222-22-222-22-2-2-2-22-222002-2-2200002-2-22000000000002-2-2200000000000000000000000000002i−2i2i−2i000
χ502-2-222-22-222-22-2-2-2-22-222002-2-2200002-2-22000000000002-2-220000000000000000000000000000−2i2i−2i2i000
χ512-2-222-22-222-22-2-2-2-22-22200-222-200002-2-2200000000000-222-200000000000000000000000000002i−2i−2i2i000
χ522-2-222-22-222-22-2-2-2-22-22200-222-200002-2-2200000000000-222-20000000000000000000000000000−2i2i2i−2i000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-2440000-2-2-2-222220000-4000022000000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-4000022222222000040000-2-2000000000000000000000000000000000000000
χ55444-4-4-44-4400004-44-4-44-400000000000000000000000000000000000000000004-40000000000000000000
χ56444-4-4-44-4400004-44-4-44-40000000000000000000000000000000000000000000-440000000000000000000
χ5744-44-4-4-44400004-4-444-4-40000000000000000000000000000000000000000000000000000000000000−2i22i20
χ5844-44-4-4-44400004-4-444-4-400000000000000000000000000000000000000000000000000000000000002i2−2i20
χ5944-4-444-4-44-444-444-4-4-4-440000000000-44-4400000000000000000000000000000000000000000000000000
χ6044-4-444-4-4-2-444-4-2-22222-20000002323−23−232-22-2000000000−2323000000000000000000000000000000000000000
χ6144-4-444-4-4-2-444-4-2-22222-2000000−23−2323232-22-200000000023−23000000000000000000000000000000000000000
χ624-444-44-4-440000-4444-4-4-44-400004-44-4000000000000000000000000000000000000000000000000000000
χ634-444-44-4-440000-4444-4-4-4-440000-44-44000000000000000000000000000000000000000000000000000000
χ644-444-44-4-4-200002-2-2-22224-40000-22-2200000000000000000000000i6−i6i6−i6i6−i6i6−i600000000000000000000000
χ654-444-44-4-4-200002-2-2-22224-40000-22-2200000000000000000000000−i6i6−i6i6−i6i6−i6i600000000000000000000000
χ664-444-44-4-4-200002-2-2-2222-4400002-22-200000000000000000000000i6−i6i6−i6−i6i6−i6i600000000000000000000000
χ674-444-44-4-4-200002-2-2-2222-4400002-22-200000000000000000000000−i6i6−i6i6i6−i6i6−i600000000000000000000000
χ684-44-44-4-44-244-4-422-22-22-2004i−4i4i−4i0000-2-22200000000000−2i2i−2i2i00000000000000000000000000000000000
χ694-44-44-4-44-244-4-422-22-22-200−4i4i−4i4i0000-2-222000000000002i−2i2i−2i00000000000000000000000000000000000
χ704-44-44-4-44-2-4-44422-22-22-2000000000022-2-24-40000000000000-22-220000000000000000000000000000000
χ714-44-44-4-44-2-4-44422-22-22-2000000000022-2-2-4400000000000002-22-20000000000000000000000000000000
χ724-4-444-44-44-44-44-4-4-44-4440000000000-444-400000000000000000000000000000000000000000000000000
χ734-4-444-44-4-24-44-4222-22-2-2004-4-440000-222-200000000000-222-200000000000000000000000000000000000
χ744-4-444-44-4-24-44-4222-22-2-200-444-40000-222-2000000000002-2-2200000000000000000000000000000000000
χ754-4-444-44-4-2-44-44222-22-2-200000000002-2-22000000000000000−2i32i32i3−2i30000000000000000000000000000000
χ764-4-444-44-4-2-44-44222-22-2-200000000002-2-220000000000000002i3−2i3−2i32i30000000000000000000000000000000
χ774-4-4-4-444440000-44-4-444-400000000000000000000022−220000000000000022−22−222200000000000000000000000
χ784-4-4-4-444440000-44-4-444-4000000000000000000000−222200000000000000−222222−2200000000000000000000000
χ794-4-4-4-4444-200002-222-2-2200000023−23−23230000000000022−2200000000006−6−66−222−200000000000000000000000
χ804-4-4-4-4444-200002-222-2-2200000023−23−232300000000000−22220000000000−666−62−2−2200000000000000000000000
χ814-4-4-4-4444-200002-222-2-22000000−232323−230000000000022−220000000000−666−6−222−200000000000000000000000
χ824-4-4-4-4444-200002-222-2-22000000−232323−2300000000000−222200000000006−6−662−2−2200000000000000000000000
χ83888-8-8-88-8-40000-44-444-440000000000000000000000000000000000000000000000000000000000000000
χ8488-88-8-8-88-40000-444-4-4440000000000000000000000000000000000000000000000000000000000000000

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