Finite Group Databasebeta

← Group #10876009

Character table — Group #10876009

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222444444444444448888888888888888888888888881212121212121616161616242424242424242424242448
order122222223444466666662222441212121212121212444446666888812121212121224242424242424244444442661212444444488884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-11111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-111111-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-11111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111
χ5111111111111111111111111-1-111-1-1-1-11111-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-111-1-1-1111111-1-1-1
χ6111111111111111111111111-1-111-1-1-1-11111-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-111111-1-1-1-1-1-1111
χ7111111111111111111111111-1-111-1-1-1-111-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-111111-1-1-1-1-111-1-1-1-1111
χ8111111111111111111111111-1-111-1-1-1-111-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1111-1-1111-1-11111-1-1-1
χ911111111111111111111-1-1-1-1111111111111-1-11-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-11
χ1011111111111111111111-1-1-1-1111111111111-1-11-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-11111-1-11111-1
χ1111111111111111111111-1-1-1-11111111111-1-1-1-11-1-1-1-1111111-1-1-1-111111111111111-1-1-1-1-11-1-1-1-1-1-11111-1
χ1211111111111111111111-1-1-1-11111111111-1-1-1-11-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11
χ1311111111111111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-111-1-11111-1-1-1-1111111-1-111-1-1-111-111-1-111-1-111-1
χ1411111111111111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-111-1-1-1-1-1111-1-111-1-111-1-11
χ1511111111111111111111-1-1-1-1-1-111-1-1-1-111-1-111-1-1-1-1-111-1-1-1-111111111-1-1-1-111-1-111111-1-1-111-1-1-1-111-1-11
χ1611111111111111111111-1-1-1-1-1-111-1-1-1-111-1-111-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111-1-1111-1-11-1-11111-1-111-1
χ17222222222-2-2-2-22222222000022-2-22222-2-20000-200000000-2-200000000000022-2-2-2-200000200000000000
χ18222222222-2-2-2-22222222000022-2-22222-2-20000-200000000-2-2000000000000-2-2222200000-200000000000
χ19222222222-2-2-2-222222220000-2-2-2-2-2-2-2-2-2-20000200000000220000000000002222-2-200000-200000000000
χ20222222222-2-2-2-222222220000-2-2-2-2-2-2-2-2-2-2000020000000022000000000000-2-2-2-22200000200000000000
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
χ2222222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-2-2222-1-1-1-1-2-2-2-2-1-1-1-1-1-111111111000000-21111000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-1-11111-1-122-2-2-2-1-1-1-122-2-2111111-1-1-1-11111000000-211-1-1000000000000
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
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-122-2-221111-2-2-2-2-1-11111111111110000002-1-1-1-1000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-1-2-2-2-2211112222-1-11111-1-1-1-1-1-1-1-1000000-21111000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111-1-12222-21111-2-22211-1-1-1-11111-1-1-1-1000000-211-1-1000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111-1-1-2-222-2111122-2-211-1-1-1-1-1-1-1-111110000002-1-111000000000000
χ29222-2-2-2-222-22-2222-22-2-2-222-2-2002-200002-22i−2i00022-2-22i−2i000000002i2i−2i−2i00000000000002i−2i000000000000
χ30222-2-2-2-222-22-2222-22-2-2-222-2-2002-200002-2−2i2i00022-2-2−2i2i00000000−2i−2i2i2i0000000000000−2i2i000000000000
χ31222-2-2-2-222-22-2222-22-2-2-2-2-222002-200002-22i−2i000-2-222−2i2i00000000−2i−2i2i2i00000000000002i−2i000000000000
χ32222-2-2-2-222-22-2222-22-2-2-2-2-222002-200002-2−2i2i000-2-2222i−2i000000002i2i−2i−2i0000000000000−2i2i000000000000
χ33222-2-2-2-22-1-22-22-1-11-111122-2-200-1133−3−3-112i−2i000-1-1112i−2i003−333−3−3−i−iii−i3−i3i3i30000000−i3i3−ii000000000000
χ34222-2-2-2-22-1-22-22-1-11-111122-2-200-1133−3−3-11−2i2i000-1-111−2i2i003−333−3−3ii−i−ii3i3−i3−i30000000i3−i3i−i000000000000
χ35222-2-2-2-22-1-22-22-1-11-111122-2-200-11−3−333-112i−2i000-1-1112i−2i00−33−3−333−i−iiii3i3−i3−i30000000i3−i3−ii000000000000
χ36222-2-2-2-22-1-22-22-1-11-111122-2-200-11−3−333-11−2i2i000-1-111−2i2i00−33−3−333ii−i−i−i3−i3i3i30000000−i3i3i−i000000000000
χ37222-2-2-2-22-1-22-22-1-11-1111-2-22200-1133−3−3-112i−2i00011-1-1−2i2i003−3−3−333ii−i−ii3i3−i3−i30000000−i3i3−ii000000000000
χ38222-2-2-2-22-1-22-22-1-11-1111-2-22200-1133−3−3-11−2i2i00011-1-12i−2i003−3−3−333−i−iii−i3−i3i3i30000000i3−i3i−i000000000000
χ39222-2-2-2-22-1-22-22-1-11-1111-2-22200-11−3−333-112i−2i00011-1-1−2i2i00−3333−3−3ii−i−i−i3−i3i3i30000000i3−i3−ii000000000000
χ40222-2-2-2-22-1-22-22-1-11-1111-2-22200-11−3−333-11−2i2i00011-1-12i−2i00−3333−3−3−i−iiii3i3−i3−i30000000−i3i3i−i000000000000
χ412-222-22-2-222-2-22-2-222-22-2000000220000-2-2002i−2i000000000002i−2i2i−2i000000002i−2i002i−2i0000002-2000000000
χ422-222-22-2-222-2-22-2-222-22-2000000220000-2-2002i−2i000000000002i−2i2i−2i00000000−2i2i00−2i2i000000-22000000000
χ432-222-22-2-222-2-22-2-222-22-2000000220000-2-200−2i2i00000000000−2i2i−2i2i000000002i−2i002i−2i000000-22000000000
χ442-222-22-2-222-2-22-2-222-22-2000000220000-2-200−2i2i00000000000−2i2i−2i2i00000000−2i2i00−2i2i0000002-2000000000
χ452-222-22-2-22-222-2-2-222-22-22-22-200-2-2000022000002-22-20000000000000000002i−2i00−2i2i000000002i−2i0000000
χ462-222-22-2-22-222-2-2-222-22-22-22-200-2-2000022000002-22-2000000000000000000−2i2i002i−2i00000000−2i2i0000000
χ472-222-22-2-22-222-2-2-222-22-2-22-2200-2-200002200000-22-220000000000000000002i−2i00−2i2i00000000−2i2i0000000
χ482-222-22-2-22-222-2-2-222-22-2-22-2200-2-200002200000-22-22000000000000000000−2i2i002i−2i000000002i−2i0000000
χ492-22-22-22-2222-2-2-2-2-222-222-2-2200-2200002-2000002-2-2200000000000000000000000000000000002i−2i2i−2i000
χ502-22-22-22-2222-2-2-2-2-222-222-2-2200-2200002-2000002-2-220000000000000000000000000000000000−2i2i−2i2i000
χ512-22-22-22-2222-2-2-2-2-222-22-222-200-2200002-200000-222-200000000000000000000000000000000002i−2i−2i2i000
χ522-22-22-22-2222-2-2-2-2-222-22-222-200-2200002-200000-222-20000000000000000000000000000000000−2i2i2i−2i000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-200004422-2-2-2-2220000-4000000002200000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-20000-4-4222222220000400000000-2-200000000000000000000000000000000000
χ55444-4-4-4-4444-44-444-44-4-4-4000000-440000-4400000000000000000000000000000000000000000000000000
χ56444-4-4-4-44-24-44-4-2-22-22220000002-22323−23−232-20000000000000−232300000000000000000000000000000000000
χ57444-4-4-4-44-24-44-4-2-22-22220000002-2−23−2323232-2000000000000023−2300000000000000000000000000000000000
χ5844-44-4-44-4400004-4-4-444-400000000000000000000000000000000000000000004i−4i0000000000000000000
χ5944-44-4-44-4400004-4-4-444-40000000000000000000000000000000000000000000−4i4i0000000000000000000
χ6044-4-444-4-4400004-44-4-4-440000000000000000000000000000000000000000000000000000000000000−2i22i20
χ6144-4-444-4-4400004-44-4-4-4400000000000000000000000000000000000000000000000000000000000002i2−2i20
χ624-444-44-4-4-24-4-4422-2-22-22000000-2-2000022004i−4i00000000000−2i2i−2i2i0000000000000000000000000000000
χ634-444-44-4-4-24-4-4422-2-22-22000000-2-200002200−4i4i000000000002i−2i2i−2i0000000000000000000000000000000
χ644-444-44-4-4-2-444-422-2-22-224-44-400220000-2-200000-22-2200000000000000000000000000000000000000000
χ654-444-44-4-4-2-444-422-2-22-22-44-4400220000-2-2000002-22-200000000000000000000000000000000000000000
χ664-44-44-44-44-4-444-4-4-444-440000004-40000-4400000000000000000000000000000000000000000000000000
χ674-44-44-44-4-244-4-4222-2-22-24-4-44002-20000-2200000-222-200000000000000000000000000000000000000000
χ684-44-44-44-4-244-4-4222-2-22-2-444-4002-20000-22000002-2-2200000000000000000000000000000000000000000
χ694-44-44-44-4-2-4-444222-2-22-2000000-2200002-2000000000000000−2i32i32i3−2i30000000000000000000000000000000
χ704-44-44-44-4-2-4-444222-2-22-2000000-2200002-20000000000000002i3−2i3−2i32i30000000000000000000000000000000
χ714-4-444-4-4440000-44-4-4-44400004-4004-44-40000000000000000000000000000000000000000000000000000
χ724-4-444-4-4440000-44-4-4-4440000-4400-44-440000000000000000000000000000000000000000000000000000
χ734-4-444-4-44-200002-2222-2-200004-400-22-22000000000000000000000i6−i6i6−i6i6−i6i6−i600000000000000000000000
χ744-4-444-4-44-200002-2222-2-200004-400-22-22000000000000000000000−i6i6−i6i6−i6i6−i6i600000000000000000000000
χ754-4-444-4-44-200002-2222-2-20000-44002-22-2000000000000000000000i6−i6i6−i6−i6i6−i6i600000000000000000000000
χ764-4-444-4-44-200002-2222-2-20000-44002-22-2000000000000000000000−i6i6−i6i6i6−i6i6−i600000000000000000000000
χ774-4-4-4-444440000-444-44-4-4000000000000000000000000022−22000000000022−22−222200000000000000000000000
χ784-4-4-4-444440000-444-44-4-40000000000000000000000000−22220000000000−222222−2200000000000000000000000
χ794-4-4-4-4444-200002-2-22-2220000000023−23−2323000000000000022−220000006−6−66−222−200000000000000000000000
χ804-4-4-4-4444-200002-2-22-2220000000023−23−23230000000000000−2222000000−666−62−2−2200000000000000000000000
χ814-4-4-4-4444-200002-2-22-22200000000−232323−23000000000000022−22000000−666−6−222−200000000000000000000000
χ824-4-4-4-4444-200002-2-22-22200000000−232323−230000000000000−22220000006−6−662−2−2200000000000000000000000
χ8388-88-8-88-8-40000-4444-4-440000000000000000000000000000000000000000000000000000000000000000
χ8488-8-888-8-8-40000-44-4444-40000000000000000000000000000000000000000000000000000000000000000

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