Finite Group Databasebeta

← Group #10875956

Character table — Group #10875956

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222444444444444448888888888888888888888888881212121212121616161616242424242424242424242448
order12222222344446666666222244121212121212121244444666688881212121212122424242424242424444444412121212444444488882
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-11-1-11111-1-1-1-1-1
χ41111111111111111111111111111111111111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111
χ5111111111111111111111111-1-111-1-1-1-111-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-111-11111-1-1-1-111-1
χ6111111111111111111111111-1-111-1-1-1-111-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1111-1-1-1-11111-1-11
χ7111111111111111111111111-1-111-1-1-1-111-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1111-1-1-1-1-111-1-111-1-11
χ8111111111111111111111111-1-111-1-1-1-111-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1111-1-111-1-111-1
χ911111111111111111111-1-1-1-111111111111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11
χ1011111111111111111111-1-1-1-111111111111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-111111111-1
χ1111111111111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111111111-1-1-1-1-11-1-1-1-1-1-11111-1
χ1211111111111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11
χ1311111111111111111111-1-1-1-1-1-111-1-1-1-111-11111-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-111-111-1-11111-1-1-1
χ1411111111111111111111-1-1-1-1-1-111-1-1-1-111-11111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1-1111-1-111-1-1-1-1111
χ1511111111111111111111-1-1-1-1-1-111-1-1-1-111-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1111-1-1-1-1-1-1-111-1-1111
χ1611111111111111111111-1-1-1-1-1-111-1-1-1-111-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-111111-1-111-1-1-1
χ17222222222-2-2-2-22222222000022-2-22222-2-2-2000000000000-2-200000000000022-2-2-2-200000200000000000
χ18222222222-2-2-2-22222222000022-2-22222-2-2-2000000000000-2-2000000000000-2-2222200000-200000000000
χ19222222222-2-2-2-222222220000-2-2-2-2-2-2-2-2-2-220000000000002200000000000022-2-22200000-200000000000
χ20222222222-2-2-2-222222220000-2-2-2-2-2-2-2-2-2-2200000000000022000000000000-2-222-2-200000200000000000
χ2122222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-122222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-10000002-1-1-1-1000000000000
χ2222222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1222-2-2-1-1-1-1-2-2-2-2-1-1-1-1-1-111111111000000-21111000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-1-11111-1-1-2-2-222-1-1-1-122-2-2111111-1-1-1-11111000000-211-1-1000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-1-11111-1-1-2-2-2-2-2-1-1-1-1-2-2221111111111-1-1-1-10000002-1-111000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-12-2-2221111-2-2-2-2-1-11111111111110000002-1-1-1-1000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-12-2-2-2-211112222-1-11111-1-1-1-1-1-1-1-1000000-21111000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111-1-1-222221111-2-22211-1-1-1-11111-1-1-1-1000000-211-1-1000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111-1-1-222-2-2111122-2-211-1-1-1-1-1-1-1-111110000002-1-111000000000000
χ29222-2-2-22-22-2-2222-2-22-22-222-2-2002-200002-20002i−2i22-2-22i−2i000000002i2i−2i−2i00000000000002i−2i000000000000
χ30222-2-2-22-22-2-2222-2-22-22-222-2-2002-200002-2000−2i2i22-2-2−2i2i00000000−2i−2i2i2i0000000000000−2i2i000000000000
χ31222-2-2-22-22-2-2222-2-22-22-2-2-222002-200002-20002i−2i-2-222−2i2i00000000−2i−2i2i2i00000000000002i−2i000000000000
χ32222-2-2-22-22-2-2222-2-22-22-2-2-222002-200002-2000−2i2i-2-2222i−2i000000002i2i−2i−2i0000000000000−2i2i000000000000
χ33222-2-2-22-2-1-2-222-111-11-1122-2-200-1133−3−3-110002i−2i-1-1112i−2i003−333−3−3−i−iii−i3−i3i3i30000000−i3i3−ii000000000000
χ34222-2-2-22-2-1-2-222-111-11-1122-2-200-1133−3−3-11000−2i2i-1-111−2i2i003−333−3−3ii−i−ii3i3−i3−i30000000i3−i3i−i000000000000
χ35222-2-2-22-2-1-2-222-111-11-1122-2-200-11−3−333-110002i−2i-1-1112i−2i00−33−3−333−i−iiii3i3−i3−i30000000i3−i3−ii000000000000
χ36222-2-2-22-2-1-2-222-111-11-1122-2-200-11−3−333-11000−2i2i-1-111−2i2i00−33−3−333ii−i−i−i3−i3i3i30000000−i3i3i−i000000000000
χ37222-2-2-22-2-1-2-222-111-11-11-2-22200-1133−3−3-110002i−2i11-1-1−2i2i003−3−3−333ii−i−ii3i3−i3−i30000000−i3i3−ii000000000000
χ38222-2-2-22-2-1-2-222-111-11-11-2-22200-1133−3−3-11000−2i2i11-1-12i−2i003−3−3−333−i−iii−i3−i3i3i30000000i3−i3i−i000000000000
χ39222-2-2-22-2-1-2-222-111-11-11-2-22200-11−3−333-110002i−2i11-1-1−2i2i00−3333−3−3ii−i−i−i3−i3i3i30000000i3−i3−ii000000000000
χ40222-2-2-22-2-1-2-222-111-11-11-2-22200-11−3−333-11000−2i2i11-1-12i−2i00−3333−3−3−i−iiii3i3−i3−i30000000−i3i3i−i000000000000
χ412-2222-2-2-222-2-22-2-2-222-22000000-2200002-202-20000000000002-22-2000000002i−2i2i−2i0000000000002i−2i00000
χ422-2222-2-2-222-2-22-2-2-222-22000000-2200002-202-20000000000002-22-200000000−2i2i−2i2i000000000000−2i2i00000
χ432-2222-2-2-222-2-22-2-2-222-22000000-2200002-20-22000000000000-22-22000000002i−2i2i−2i000000000000−2i2i00000
χ442-2222-2-2-222-2-22-2-2-222-22000000-2200002-20-22000000000000-22-2200000000−2i2i−2i2i0000000000002i−2i00000
χ452-2222-2-2-22-222-2-2-2-222-222-22-2002-20000-22000002-22-20000000000000000002i−2i−2i2i00000000002i−2i0000000
χ462-2222-2-2-22-222-2-2-2-222-222-22-2002-20000-22000002-22-2000000000000000000−2i2i2i−2i0000000000−2i2i0000000
χ472-2222-2-2-22-222-2-2-2-222-22-22-22002-20000-2200000-22-220000000000000000002i−2i−2i2i0000000000−2i2i0000000
χ482-2222-2-2-22-222-2-2-2-222-22-22-22002-20000-2200000-22-22000000000000000000−2i2i2i−2i00000000002i−2i0000000
χ492-22-2-22-2222-22-2-2222-2-2-22-2-2200220000-2-2000002-2-220000000000000000000000000000002i−2i0000002i−2i0
χ502-22-2-22-2222-22-2-2222-2-2-22-2-2200220000-2-2000002-2-22000000000000000000000000000000−2i2i000000−2i2i0
χ512-22-2-22-2222-22-2-2222-2-2-2-222-200220000-2-200000-222-20000000000000000000000000000002i−2i000000−2i2i0
χ522-22-2-22-2222-22-2-2222-2-2-2-222-200220000-2-200000-222-2000000000000000000000000000000−2i2i0000002i−2i0
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-200004422-2-2-2-222-40000000000002200000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-20000-4-4222222224000000000000-2-200000000000000000000000000000000000
χ55444-4-4-44-4444-4-44-4-44-44-4000000-440000-4400000000000000000000000000000000000000000000000000
χ56444-4-4-44-4-244-4-4-222-22-220000002-22323−23−232-20000000000000−232300000000000000000000000000000000000
χ57444-4-4-44-4-244-4-4-222-22-220000002-2−23−2323232-2000000000000023−2300000000000000000000000000000000000
χ5844-44-44-4-44000044-4-44-4-40000000000000000000000000000000000000000000000000000000000022−22000
χ5944-44-44-4-44000044-4-44-4-400000000000000000000000000000000000000000000000000000000000−2222000
χ6044-4-44-4-44400004-44-4-4-440000000000000000000000000000000000000000000004-400000000000000000
χ6144-4-44-4-44400004-44-4-4-44000000000000000000000000000000000000000000000-4400000000000000000
χ624-4444-4-4-4-24-4-44222-2-22-20000002-20000-2204-4000000000000-22-220000000000000000000000000000000
χ634-4444-4-4-4-24-4-44222-2-22-20000002-20000-220-440000000000002-22-20000000000000000000000000000000
χ644-4444-4-4-4-2-444-4222-2-22-24-44-400-2200002-200000-22-2200000000000000000000000000000000000000000
χ654-4444-4-4-4-2-444-4222-2-22-2-44-4400-2200002-2000002-22-200000000000000000000000000000000000000000
χ664-44-4-44-444-44-44-4444-4-4-4000000-4-400004400000000000000000000000000000000000000000000000000
χ674-44-4-44-44-24-44-42-2-2-22224-4-4400-2-200002200000-222-200000000000000000000000000000000000000000
χ684-44-4-44-44-24-44-42-2-2-2222-444-400-2-2000022000002-2-2200000000000000000000000000000000000000000
χ694-44-4-44-44-2-44-442-2-2-2222000000220000-2-200000000000000023−23−23230000000000000000000000000000000
χ704-44-4-44-44-2-44-442-2-2-2222000000220000-2-2000000000000000−232323−230000000000000000000000000000000
χ714-4-44-4-44440000-4-44-444-4000000000000000000000000022−22000000000022−2222−2200000000000000000000000
χ724-4-44-4-44440000-4-44-444-40000000000000000000000000−22220000000000−2222−222200000000000000000000000
χ734-4-44-4-444-2000022-22-2-220000000023−2323−23000000000000022−220000006−66−6−22−2200000000000000000000000
χ744-4-44-4-444-2000022-22-2-220000000023−2323−230000000000000−2222000000−66−662−22−200000000000000000000000
χ754-4-44-4-444-2000022-22-2-2200000000−2323−2323000000000000022−22000000−66−66−22−2200000000000000000000000
χ764-4-44-4-444-2000022-22-2-2200000000−2323−23230000000000000−22220000006−66−62−22−200000000000000000000000
χ774-4-4-4444-440000-44-4-4-44400004-4004-4-440000000000000000000000000000000000000000000000000000
χ784-4-4-4444-440000-44-4-4-4440000-4400-444-40000000000000000000000000000000000000000000000000000
χ794-4-4-4444-4-200002-2222-2-200004-400-222-2000000000000000000000i6−i6−i6i6i6−i6−i6i600000000000000000000000
χ804-4-4-4444-4-200002-2222-2-200004-400-222-2000000000000000000000−i6i6i6−i6−i6i6i6−i600000000000000000000000
χ814-4-4-4444-4-200002-2222-2-20000-44002-2-22000000000000000000000i6−i6−i6i6−i6i6i6−i600000000000000000000000
χ824-4-4-4444-4-200002-2222-2-20000-44002-2-22000000000000000000000−i6i6i6−i6i6−i6−i6i600000000000000000000000
χ8388-88-88-8-8-40000-4-444-4440000000000000000000000000000000000000000000000000000000000000000
χ8488-8-88-8-88-40000-44-4444-40000000000000000000000000000000000000000000000000000000000000000

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