Finite Group Databasebeta

← Group #10711770

Character table — Group #10711770

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1122222222222224444444444444444488888888888816161616161616161616161624242424242424242424242424242424
order122223444468812122244666888121212242424246688121224242424242444881212121224242424444444441616161616161616
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111-1-1-1-11111111111111-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111111-1-1-1-11111111111111-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111-1-1-1-11111111111111-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ8111111111111111-1-1-1-11111111111111-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ9111-1-111-11-1111-1-11-11-11-1-1-1-111-1111-1-11-11-11-11-111-1-1i−ii−iii−i−iii−i−iii−i−iii−i−i11-1-111-1-1
χ10111-1-111-11-1111-1-11-11-11-1-1-1-111-1111-1-11-11-11-11-111-1-1i−ii−iii−i−iii−i−i−i−iii−i−iii-1-111-1-111
χ11111-1-111-11-1111-1-11-11-11-1-1-1-111-1111-1-11-11-11-11-111-1-1−ii−ii−i−iii−i−iiiii−i−iii−i−i-1-111-1-111
χ12111-1-111-11-1111-1-11-11-11-1-1-1-111-1111-1-11-11-11-11-111-1-1−ii−ii−i−iii−i−iii−i−iii−i−iii11-1-111-1-1
χ13111-1-111-11-1111-1-1-11-111-1-1-1-111-1111-1-1-11-11-111-1-1-111i−i−iiii−i−i−i−iiiii−i−i−i−iii11-1-1-1-111
χ14111-1-111-11-1111-1-1-11-111-1-1-1-111-1111-1-1-11-11-111-1-1-111i−i−iiii−i−i−i−iii−i−iiiii−i−i-1-11111-1-1
χ15111-1-111-11-1111-1-1-11-111-1-1-1-111-1111-1-1-11-11-111-1-1-111−iii−i−i−iiiii−i−iii−i−i−i−iii-1-11111-1-1
χ16111-1-111-11-1111-1-1-11-111-1-1-1-111-1111-1-1-11-11-111-1-1-111−iii−i−i−iiiii−i−i−i−iiiii−i−i11-1-1-1-111
χ1722222222222-2-2222222222-2-2-2222-2-2-2-222-2-222-2-2-2-2-2-20000000000000000000000000000
χ1822222222222-2-222-2-2-2-2222-2-2-2222-2-2-2-2-2-222-2-2-2-222220000000000000000000000000000
χ1922222-12222-122-1-12222-1-1-1222-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000000000
χ2022222-12222-122-1-12222-1-1-1222-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000000000
χ2122222-12222-122-1-1-2-2-2-2-1-1-1222-1-1-1-1-1-1-111-2-211-1-1111122-2-2-1-1-1-111110000000000000000
χ2222222-12222-122-1-1-2-2-2-2-1-1-1222-1-1-1-1-1-1-111-2-211-1-11111-2-2221111-1-1-1-10000000000000000
χ2322222-12222-1-2-2-1-12222-1-1-1-2-2-2-1-1-11111-1-1-2-2-1-11111110000−i3i3−i3i3−i3i3−i3i30000000000000000
χ2422222-12222-1-2-2-1-12222-1-1-1-2-2-2-1-1-11111-1-1-2-2-1-11111110000i3−i3i3−i3i3−i3i3−i30000000000000000
χ2522222-12222-1-2-2-1-1-2-2-2-2-1-1-1-2-2-2-1-1-1111111221111-1-1-1-10000−i3i3−i3i3i3−i3i3−i30000000000000000
χ2622222-12222-1-2-2-1-1-2-2-2-2-1-1-1-2-2-2-1-1-1111111221111-1-1-1-10000i3−i3i3−i3−i3i3−i3i30000000000000000
χ27222-2-222-22-22-2-2-2-22-22-22-2-222-22-22-2-2222-2-222-2-22-2-2220000000000000000000000000000
χ28222-2-222-22-22-2-2-2-2-22-222-2-222-22-22-2-222-222-2-22-2222-2-20000000000000000000000000000
χ29222-2-2-12-22-2-122112-22-2-111-2-22-11-1-1-111-112-2-11-11-1-1112i−2i2i−2i−i−iii−i−iii0000000000000000
χ30222-2-2-12-22-2-122112-22-2-111-2-22-11-1-1-111-112-2-11-11-1-111−2i2i−2i2iii−i−iii−i−i0000000000000000
χ31222-2-2-12-22-2-12211-22-22-111-2-22-11-1-1-1111-1-221-1-1111-1-12i−2i−2i2i−i−iiiii−i−i0000000000000000
χ32222-2-2-12-22-2-12211-22-22-111-2-22-11-1-1-1111-1-221-1-1111-1-1−2i2i2i−2iii−i−i−i−iii0000000000000000
χ33222-2-2-12-22-2-1-2-2112-22-2-11122-2-11-111-1-1-11-22-111-111-1-100003−3−333−3−330000000000000000
χ34222-2-2-12-22-2-1-2-2112-22-2-11122-2-11-111-1-1-11-22-111-111-1-10000−333−3−333−30000000000000000
χ35222-2-2-12-22-2-1-2-211-22-22-11122-2-11-111-1-11-12-21-11-1-1-11100003−3−33−333−30000000000000000
χ36222-2-2-12-22-2-1-2-211-22-22-11122-2-11-111-1-11-12-21-11-1-1-1110000−333−33−3−330000000000000000
χ3722-22-222-2-22200222-2-22-2-220002-2-200002-200-2200000000000000000000000000−i2i2−i2i2−i2i2−i2i2
χ3822-22-222-2-22200222-2-22-2-220002-2-200002-200-2200000000000000000000000000i2−i2i2−i2i2−i2i2−i2
χ3922-22-222-2-2220022-222-2-2-220002-2-20000-22002-200000000000000000000000000−i2i2−i2i2i2−i2i2−i2
χ4022-22-222-2-2220022-222-2-2-220002-2-20000-22002-200000000000000000000000000i2−i2i2−i2−i2i2−i2i2
χ4122-22-22-222-2222-2-20000-2-222-2-2-22222-2-2000000-22000000000000000000002i−2i2i−2i00000000
χ4222-22-22-222-2222-2-20000-2-222-2-2-22222-2-2000000-2200000000000000000000−2i2i−2i2i00000000
χ4322-22-22-222-22-2-2-2-20000-2-22-222-222-2-2220000002-200000000000000002i−2i2i−2i000000000000
χ4422-22-22-222-22-2-2-2-20000-2-22-222-222-2-2220000002-20000000000000000−2i2i−2i2i000000000000
χ4522-2-22222-2-2200-2-222-2-2-22-200022-200002200-2-200000000000000000000000000−i2i2i2−i2−i2i2i2−i2
χ4622-2-22222-2-2200-2-222-2-2-22-200022-200002200-2-200000000000000000000000000i2−i2−i2i2i2−i2−i2i2
χ4722-2-22222-2-2200-2-2-2-222-22-200022-20000-2-2002200000000000000000000000000−i2i2i2−i2i2−i2−i2i2
χ4822-2-22222-2-2200-2-2-2-222-22-200022-20000-2-2002200000000000000000000000000i2−i2−i2i2−i2i2i2−i2
χ4922-2-222-2-222222220000-22-2-22-2-2-222222000000-2-2000000000000000000002-2-2200000000
χ5022-2-222-2-222222220000-22-2-22-2-2-222222000000-2-200000000000000000000-222-200000000
χ5122-2-222-2-2222-2-2220000-22-22-22-2-22-2-2-2-20000002200000000000000002-2-22000000000000
χ5222-2-222-2-2222-2-2220000-22-22-22-2-22-2-2-2-2000000220000000000000000-222-2000000000000
χ53444444-4-4-4-4400-4-40000444000-4-4-400000000000000000000000000000000000000000000
χ5444444-2-4-4-4-4-200220000-2-2-200022200000000000023−2323−230000000000000000000000000000
χ5544444-2-4-4-4-4-200220000-2-2-2000222000000000000−2323−23230000000000000000000000000000
χ56444-4-44-44-444004400004-4-4000-44-400000000000000000000000000000000000000000000
χ57444-4-4-2-44-44-200-2-20000-2220002-2200000000000023−23−23230000000000000000000000000000
χ58444-4-4-2-44-44-200-2-20000-2220002-22000000000000−232323−230000000000000000000000000000
χ5944-44-4-24-4-44-200-2-24-4-4422-2000-2220000-22002-20000000000000000000000000000000000
χ6044-44-4-24-4-44-200-2-2-444-422-2000-22200002-200-220000000000000000000000000000000000
χ6144-44-4-2-444-4-24422000022-24-4-42-2-2-2-2220000002-200000000000000000000000000000000
χ6244-44-4-2-444-4-2-4-422000022-2-4442-2-222-2-2000000-2200000000000000000000000000000000
χ6344-4-44-244-4-4-2002244-4-42-22000-2-220000-2-200220000000000000000000000000000000000
χ6444-4-44-244-4-4-20022-4-4442-22000-2-2200002200-2-20000000000000000000000000000000000
χ6544-4-44-2-4-444-244-2-200002-22-44-422-2-2-2-2-20000002200000000000000000000000000000000
χ6644-4-44-2-4-444-2-4-4-2-200002-224-4422-22222000000-2-200000000000000000000000000000000
χ678-800080000-8−4i24i2000000000000000−4i24i2000000000000000000000000000000000000000000
χ688-800080000-84i2−4i20000000000000004i2−4i2000000000000000000000000000000000000000000
χ698-8000-400004−4i24i243−4300000000000002i2−2i22i6−2i60000000000000000000000000000000000000000
χ708-8000-400004−4i24i2−434300000000000002i2−2i2−2i62i60000000000000000000000000000000000000000
χ718-8000-4000044i2−4i243−430000000000000−2i22i2−2i62i60000000000000000000000000000000000000000
χ728-8000-4000044i2−4i2−43430000000000000−2i22i22i6−2i60000000000000000000000000000000000000000

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