Finite Group Databasebeta

← Group #10868231

Character table — Group #10868231

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222444444444444448888888888888888888888888881212121212121616161616242424242424242424242448
order1222222234444666666644444412121212121212122444466888812121212121212122424242424242424444444412121212224444488884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1111-1-111-1-1-1-1-1
χ41111111111111111111111111111111111111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111
χ51111111111111111111111-1-1-1-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1111-1-1-1-1-1-11
χ61111111111111111111111-1-1-1-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1111111-1
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
χ911111111111111111111-1-1111111-1-1-1-111-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1-1-1-111-1-1-1-11-1-111-1-1111
χ1011111111111111111111-1-1111111-1-1-1-111-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-11111-111-1-111-111-1-111-1-1-1
χ1111111111111111111111-1-1111111-1-1-1-111-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-11-1-111-1-11111111-1-1-1
χ1211111111111111111111-1-1111111-1-1-1-111-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111111-1-11111-1-1-1-1-1-1-1111
χ1311111111111111111111-1-1-1-1-1-111-1-1-1-111-11111-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-111-1-1111-1-1-1-111-1-11
χ1411111111111111111111-1-1-1-1-1-111-1-1-1-111-11111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-11111-111-1-1-1-1-11111-1-111-1
χ1511111111111111111111-1-1-1-1-1-111-1-1-1-111-111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1-1-11-1-11111111-1-1-1-111-1
χ1611111111111111111111-1-1-1-1-1-111-1-1-1-111-111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111111-1-111-1-1-1-1-11111-1-11
χ17222222222-2-2-2-22222222220000-2-22222-2-2-20000-2-20000000000000000000022-2-2220000000-2000000000
χ18222222222-2-2-2-22222222220000-2-22222-2-2-20000-2-200000000000000000000-2-222-2-200000002000000000
χ19222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-22000022000000000000000000002222-2-20000000-2000000000
χ20222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-2200002200000000000000000000-2-2-2-22200000002000000000
χ2122222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-122222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000002-1-1-1-1000000000000
χ2222222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1222-2-2-1-1-2-2-2-2-1-1-1-1-1-1-1-111111111000000-21111000000000000
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-12-2-222-1-1-2-2-2-211111111111111110000002-1-1-1-1000000000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-12-2-2-2-2-1-1222211111111-1-1-1-1-1-1-1-1000000-21111000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-22222-1-11111-1-1-2-2-22211-2-2221111-1-1-1-1-1-1-1-11111000000-2-1-111000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-22222-1-11111-1-1-2-2-2-2-21122-2-21111-1-1-1-11111-1-1-1-1000000211-1-1000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111-1-1-222221122-2-2-1-1-1-111111111-1-1-1-1000000-2-1-111000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111-1-1-222-2-211-2-222-1-1-1-11111-1-1-1-11111000000211-1-1000000000000
χ29222-2-2-2-2222-2-222-2-222-2-20000002-200002-202i−2i000000002i2i−2i−2i000000000000002i−2i2i−2i00000000002-200000
χ30222-2-2-2-2222-2-222-2-222-2-20000002-200002-202i−2i000000002i2i−2i−2i00000000000000−2i2i−2i2i0000000000-2200000
χ31222-2-2-2-2222-2-222-2-222-2-20000002-200002-20−2i2i00000000−2i−2i2i2i000000000000002i−2i2i−2i0000000000-2200000
χ32222-2-2-2-2222-2-222-2-222-2-20000002-200002-20−2i2i00000000−2i−2i2i2i00000000000000−2i2i−2i2i00000000002-200000
χ33222-2-2-2-222-222-22-2-222-2-2002i2i−2i−2i-220000-220000000000000002i2i−2i−2i00000000002i−2i−2i2i000002-20000000000
χ34222-2-2-2-222-222-22-2-222-2-2002i2i−2i−2i-220000-220000000000000002i2i−2i−2i0000000000−2i2i2i−2i00000-220000000000
χ35222-2-2-2-222-222-22-2-222-2-200−2i−2i2i2i-220000-22000000000000000−2i−2i2i2i00000000002i−2i−2i2i00000-220000000000
χ36222-2-2-2-222-222-22-2-222-2-200−2i−2i2i2i-220000-22000000000000000−2i−2i2i2i0000000000−2i2i2i−2i000002-20000000000
χ372-222-2-22-22-22-22-2222-2-2-2002i−2i2i−2i-2-20000220002i−2i00002-200002i−2i2i−2i22-2-2000000000002i−2i00000000000000
χ382-222-2-22-22-22-22-2222-2-2-2002i−2i2i−2i-2-2000022000−2i2i0000-2200002i−2i2i−2i-2-22200000000000−2i2i00000000000000
χ392-222-2-22-22-22-22-2222-2-2-200−2i2i−2i2i-2-20000220002i−2i0000-220000−2i2i−2i2i-2-222000000000002i−2i00000000000000
χ402-222-2-22-22-22-22-2222-2-2-200−2i2i−2i2i-2-2000022000−2i2i00002-20000−2i2i−2i2i22-2-200000000000−2i2i00000000000000
χ412-222-2-22-2-1-22-221-1-1-1111002i−2i2i−2i11−i3−i3i3i3-1-10002i−2i−i3i3002-23−33−3−ii−ii-1-111−i3−i3i3i30000000−ii3−3000000000000
χ422-222-2-22-2-1-22-221-1-1-1111002i−2i2i−2i11−i3−i3i3i3-1-1000−2i2i−i3i300-223−33−3−ii−ii11-1-1i3i3−i3−i30000000i−i−33000000000000
χ432-222-2-22-2-1-22-221-1-1-1111002i−2i2i−2i11i3i3−i3−i3-1-10002i−2ii3−i3002-2−33−33−ii−ii-1-111i3i3−i3−i30000000−ii−33000000000000
χ442-222-2-22-2-1-22-221-1-1-1111002i−2i2i−2i11i3i3−i3−i3-1-1000−2i2ii3−i300-22−33−33−ii−ii11-1-1−i3−i3i3i30000000i−i3−3000000000000
χ452-222-2-22-2-1-22-221-1-1-111100−2i2i−2i2i11−i3−i3i3i3-1-10002i−2i−i3i300-22−33−33i−ii−i11-1-1i3i3−i3−i30000000−ii3−3000000000000
χ462-222-2-22-2-1-22-221-1-1-111100−2i2i−2i2i11−i3−i3i3i3-1-1000−2i2i−i3i3002-2−33−33i−ii−i-1-111−i3−i3i3i30000000i−i−33000000000000
χ472-222-2-22-2-1-22-221-1-1-111100−2i2i−2i2i11i3i3−i3−i3-1-10002i−2ii3−i300-223−33−3i−ii−i11-1-1−i3−i3i3i30000000−ii−33000000000000
χ482-222-2-22-2-1-22-221-1-1-111100−2i2i−2i2i11i3i3−i3−i3-1-1000−2i2ii3−i3002-23−33−3i−ii−i-1-111i3i3−i3−i30000000i−i3−3000000000000
χ492-22-222-2-2222-2-2-2-2-22-222002-2-222-20000-220000000000000002-2-2200000000000000000000002i−2i002i−2i000
χ502-22-222-2-2222-2-2-2-2-22-222002-2-222-20000-220000000000000002-2-220000000000000000000000−2i2i00−2i2i000
χ512-22-222-2-2222-2-2-2-2-22-22200-222-22-20000-22000000000000000-222-200000000000000000000002i−2i00−2i2i000
χ522-22-222-2-2222-2-2-2-2-22-22200-222-22-20000-22000000000000000-222-20000000000000000000000−2i2i002i−2i000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-244000022-2-2-2-222-40000220000000000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-400002222222240000-2-20000000000000000000000000000000000000000000
χ55444-4-4-4-44-24-4-44-222-2-222000000-220000-2204i−4i00000000−2i−2i2i2i00000000000000000000000000000000000
χ56444-4-4-4-44-24-4-44-222-2-222000000-220000-220−4i4i000000002i2i−2i−2i00000000000000000000000000000000000
χ57444-4-4-4-44-2-444-4-222-2-222004i4i−4i−4i2-200002-2000000000000000−2i−2i2i2i0000000000000000000000000000000
χ58444-4-4-4-44-2-444-4-222-2-22200−4i−4i4i4i2-200002-20000000000000002i2i−2i−2i0000000000000000000000000000000
χ5944-444-4-4-44000044-4-4-44-4000000000000000000000000000000000000000004-4000000000000000000000
χ6044-444-4-4-44000044-4-4-44-400000000000000000000000000000000000000000-44000000000000000000000
χ6144-4-4-444-4400004-44-4-4-444i−4i0000004i−4i4i−4i0000000000000000000000000000000000000000000000000000
χ6244-4-4-444-4400004-44-4-4-44−4i4i000000−4i4i−4i4i0000000000000000000000000000000000000000000000000000
χ6344-4-4-444-4-20000-22-2222-24i−4i000000−2i2i−2i2i0000000000000000000006−66−6i6−i6i6−i600000000000000000000000
χ6444-4-4-444-4-20000-22-2222-24i−4i000000−2i2i−2i2i000000000000000000000−66−66−i6i6−i6i600000000000000000000000
χ6544-4-4-444-4-20000-22-2222-2−4i4i0000002i−2i2i−2i0000000000000000000006−66−6−i6i6−i6i600000000000000000000000
χ6644-4-4-444-4-20000-22-2222-2−4i4i0000002i−2i2i−2i000000000000000000000−66−66i6−i6i6−i600000000000000000000000
χ674-444-4-44-444-44-4-4444-4-4-4000000440000-4-400000000000000000000000000000000000000000000000000
χ684-444-4-44-4-24-44-42-2-2-2222000000-2-2−2i3−2i32i32i322000002i3−2i30000000000000000000000000000000000000000000
χ694-444-4-44-4-24-44-42-2-2-2222000000-2-22i32i3−2i3−2i32200000−2i32i30000000000000000000000000000000000000000000
χ704-44-444-4-44-4-444-4-4-44-444000000-4400004-400000000000000000000000000000000000000000000000000
χ714-44-444-4-4-244-4-4222-22-2-2004-4-44-2200002-2000000000000000-222-20000000000000000000000000000000
χ724-44-444-4-4-244-4-4222-22-2-200-444-4-2200002-20000000000000002-2-220000000000000000000000000000000
χ734-44-444-4-4-2-4-444222-22-2-20000002-20000-2200000000000−2i32i32i3−2i300000000000000000000000000000000000
χ744-44-444-4-4-2-4-444222-22-2-20000002-20000-22000000000002i3−2i3−2i32i300000000000000000000000000000000000
χ754-4-44-44-4440000-44-4-44-44000000000000000000000000000000000000000000000000000000000000022−220
χ764-4-44-44-4440000-44-4-44-440000000000000000000000000000000000000000000000000000000000000−22220
χ774-4-4-44-44440000-4-44-444-400000000000000000000022−220000000000000022−22−222200000000000000000000000
χ784-4-4-44-44440000-4-44-444-4000000000000000000000−222200000000000000−222222−2200000000000000000000000
χ794-4-4-44-444-2000022-22-2-220000000023−23−232300000000022−220000000000−666−6−222−200000000000000000000000
χ804-4-4-44-444-2000022-22-2-220000000023−23−2323000000000−222200000000006−6−662−2−2200000000000000000000000
χ814-4-4-44-444-2000022-22-2-2200000000−232323−2300000000022−2200000000006−6−66−222−200000000000000000000000
χ824-4-4-44-444-2000022-22-2-2200000000−232323−23000000000−22220000000000−666−62−2−2200000000000000000000000
χ8388-888-8-8-8-40000-4-4444-440000000000000000000000000000000000000000000000000000000000000000
χ848-8-88-88-88-400004-444-44-40000000000000000000000000000000000000000000000000000000000000000

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