Finite Group Databasebeta

← Group #10844767

Character table — Group #10844767

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11111111222222222222444444446666888888888888888888881212121212121616161616161616161624242424242424244848
order1222222234444666666688881212121244442244448812121212242424242424242444888844661212121212124444448824
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-111-1-111-111-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-111-1-111-1-1-1-1-1-1-1-111
χ51111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11-1-111111
χ71111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-11111111111-1-1
χ911111111111111111111-1-1-1-11111111111-1-111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1111-1-1-1-111-1-11111-1-1-11
χ1011111111111111111111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-11-11111-1-1-1-1-1-1-111-1111-1
χ1111111111111111111111-1-1-1-111111111-1-11111-1-11111-1-1-1-1-1-1-1-111-1-1-1-11-1-1-11111-1-1111-1-11-1-11-1
χ1211111111111111111111-1-1-1-111111111-1-111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-11-1-1-1-1111111-1-1-1-111-11
χ1311111111111111111111-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-11111-1111-1-1-1-11111-1-1-1-1111-1
χ1411111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111111-11111-1-1-1-1111-1-11-1-1-11
χ1511111111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-111111-1-1-11111-1-1-1-1-111-111-11
χ1611111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-11111-11-1-1-1-11111-1-11111-1-11-1
χ17222222222-2-2-2-222222220000-2-2-2-2222200002-20022-2-200000000-2-20000000000000000-20020000
χ18222222222-2-2-2-222222220000-2-2-2-222220000-2200-2-22200000000-2-20000000000000000200-20000
χ19222222222-2-2-2-222222220000-2-2-2-2-2-2-2-200002-20022-2-200000000220000000000000000200-20000
χ20222222222-2-2-2-222222220000-2-2-2-2-2-2-2-20000-2200-2-22200000000220000000000000000-20020000
χ2122222222-12222-1-1-1-1-1-1-12222-1-1-1-1000022222222-1-1-1-1-1-1-1-1-1-1-1-100000022-1-1-1-1-1-1-1-10000000000
χ2222222222-12222-1-1-1-1-1-1-12222-1-1-1-100002222-2-2-2-21111-1-1-1-11111000000-2-2-1-111-1-1110000000000
χ2322222222-12222-1-1-1-1-1-1-12222-1-1-1-10000-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1000000-2-2111111110000000000
χ2422222222-12222-1-1-1-1-1-1-12222-1-1-1-10000-2-2-2-2-2-2-2-21111-1-1-1-111110000002211-1-111-1-10000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1000022-2-222-2-2-1-1-1-111111111000000-22-1-11111-1-10000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1000022-2-2-2-22211111111-1-1-1-10000002-2-1-1-1-111110000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-10000-2-22222-2-2-1-1-1-1111111110000002-211-1-1-1-1110000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-10000-2-222-2-22211111111-1-1-1-1000000-221111-1-1-1-10000000000
χ29222-22-2-2-222-2-2222-2-2-22-22i2i−2i−2i2-22-200002-22i−2i000000002i2i−2i−2i0000000000002-2002i−2i000000000000
χ30222-22-2-2-222-2-2222-2-2-22-22i2i−2i−2i2-22-20000-22−2i2i000000002i2i−2i−2i000000000000-2200−2i2i000000000000
χ31222-22-2-2-222-2-2222-2-2-22-2−2i−2i2i2i2-22-200002-2−2i2i00000000−2i−2i2i2i0000000000002-200−2i2i000000000000
χ32222-22-2-2-222-2-2222-2-2-22-2−2i−2i2i2i2-22-20000-222i−2i00000000−2i−2i2i2i000000000000-22002i−2i000000000000
χ33222-22-2-2-2-12-2-22-1-1111-112i2i−2i−2i-11-1100002-22i−2i00003−33−3−i−iii−i3−i3i3i300000000-11−i3i3−ii3−30000000000
χ34222-22-2-2-2-12-2-22-1-1111-112i2i−2i−2i-11-1100002-22i−2i0000−33−33−i−iiii3i3−i3−i300000000-11i3−i3−ii−330000000000
χ35222-22-2-2-2-12-2-22-1-1111-112i2i−2i−2i-11-110000-22−2i2i00003−33−3−i−iii−i3−i3i3i3000000001-1i3−i3i−i−330000000000
χ36222-22-2-2-2-12-2-22-1-1111-112i2i−2i−2i-11-110000-22−2i2i0000−33−33−i−iiii3i3−i3−i3000000001-1−i3i3i−i3−30000000000
χ37222-22-2-2-2-12-2-22-1-1111-11−2i−2i2i2i-11-1100002-2−2i2i00003−33−3ii−i−ii3i3−i3−i300000000-11i3−i3i−i3−30000000000
χ38222-22-2-2-2-12-2-22-1-1111-11−2i−2i2i2i-11-1100002-2−2i2i0000−33−33ii−i−i−i3−i3i3i300000000-11−i3i3i−i−330000000000
χ39222-22-2-2-2-12-2-22-1-1111-11−2i−2i2i2i-11-110000-222i−2i00003−33−3ii−i−ii3i3−i3−i3000000001-1−i3i3−ii−330000000000
χ40222-22-2-2-2-12-2-22-1-1111-11−2i−2i2i2i-11-110000-222i−2i0000−33−33ii−i−i−i3−i3i3i3000000001-1i3−i3−ii3−30000000000
χ412-222-22-2-222-22-2-2-22-2-2222-22-22-2-2200000000000000002-22-2000000000000000000002i−2i02i−2i00000
χ422-222-22-2-222-22-2-2-22-2-2222-22-22-2-2200000000000000002-22-200000000000000000000−2i2i0−2i2i00000
χ432-222-22-2-222-22-2-2-22-2-222-22-222-2-220000000000000000-22-22000000000000000000002i−2i0−2i2i00000
χ442-222-22-2-222-22-2-2-22-2-222-22-222-2-220000000000000000-22-2200000000000000000000−2i2i02i−2i00000
χ452-22-2-2-222222-2-2-2-2-2222-22i−2i−2i2i22-2-222-2-20000000000002i−2i−2i2i00002-22i2i−2i−2i00000000000000000000
χ462-22-2-2-222222-2-2-2-2-2222-22i−2i−2i2i22-2-2-2-2220000000000002i−2i−2i2i0000-22−2i−2i2i2i00000000000000000000
χ472-22-2-2-222222-2-2-2-2-2222-2−2i2i2i−2i22-2-222-2-2000000000000−2i2i2i−2i00002-2−2i−2i2i2i00000000000000000000
χ482-22-2-2-222222-2-2-2-2-2222-2−2i2i2i−2i22-2-2-2-222000000000000−2i2i2i−2i0000-222i2i−2i−2i00000000000000000000
χ492-22-2-2-2222-2-222-2-2-2222-20000-2-22222-2-20000002-2000000002-22-2-22000000000000000000002-200
χ502-22-2-2-2222-2-222-2-2-2222-20000-2-22222-2-2000000-2200000000-22-22-2200000000000000000000-2200
χ512-22-2-2-2222-2-222-2-2-2222-20000-2-222-2-2220000002-2000000002-22-22-200000000000000000000-2200
χ522-22-2-2-2222-2-222-2-2-2222-20000-2-222-2-222000000-2200000000-22-222-2000000000000000000002-200
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-200002222000000004-400-2-2220000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-20000222200000000-440022-2-20000000000000000000000000000000000
χ55444-44-4-4-44-444-444-4-4-44-40000-44-4400000000000000000000000000000000000000000000000000
χ56444-44-4-4-4-2-444-4-2-2222-2200002-22-200000000000023−23−23230000000000000000000000000000000000
χ57444-44-4-4-4-2-444-4-2-2222-2200002-22-2000000000000−232323−230000000000000000000000000000000000
χ5844-44-4-44-4400004-4-44-4-44000000004i−4i4i−4i0000000000000000000000000000000000000000000000
χ5944-44-4-44-4400004-4-44-4-4400000000−4i4i−4i4i0000000000000000000000000000000000000000000000
χ6044-4-4-44-44400004-44-44-4-40000000000000000000000000000000000−2i22i2−2i22i200000000000000000000
χ6144-4-4-44-44400004-44-44-4-400000000000000000000000000000000002i2−2i22i2−2i200000000000000000000
χ624-444-44-4-44-44-44-4-44-4-4440000-444-400000000000000000000000000000000000000000000000000
χ634-444-44-4-4-24-44-422-222-2-24-44-4-222-20000000000000000-22-22000000000000000000000000000000
χ644-444-44-4-4-24-44-422-222-2-2-44-44-222-200000000000000002-22-2000000000000000000000000000000
χ654-444-44-4-4-2-44-4422-222-2-200002-2-2200000000000000000000−2i32i32i3−2i300000000000000000000000000
χ664-444-44-4-4-2-44-4422-222-2-200002-2-22000000000000000000002i3−2i3−2i32i300000000000000000000000000
χ674-44-4-4-444-244-4-4222-2-2-224i−4i−4i4i-2-2220000000000000000−2i2i2i−2i000000000000000000000000000000
χ684-44-4-4-444-244-4-4222-2-2-22−4i4i4i−4i-2-22200000000000000002i−2i−2i2i000000000000000000000000000000
χ694-44-4-4-444-2-4-444222-2-2-22000022-2-200000000004-400000000-22-2200000000000000000000000000
χ704-44-4-4-444-2-4-444222-2-2-22000022-2-20000000000-44000000002-22-200000000000000000000000000
χ714-4-444-4-4440000-44-4-44-44000000000000000000000000000000000022−22−222200000000000000000000
χ724-4-444-4-4440000-44-4-44-440000000000000000000000000000000000−222222−2200000000000000000000
χ734-4-4-4444-440000-4444-4-4-4000000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ744-4-4-4444-440000-4444-4-4-400000000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ7588-88-8-88-8-40000-444-444-40000000000000000000000000000000000000000000000000000000000
χ7688-8-8-88-88-40000-44-44-4440000000000000000000000000000000000000000000000000000000000
χ778-8-888-8-88-400004-444-44-40000000000000000000000000000000000000000000000000000000000
χ788-8-8-8888-8-400004-4-4-44440000000000000000000000000000000000000000000000000000000000

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