Finite Group Databasebeta

← Group #10883566

Character table — Group #10883566

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1122222222222224444444444444444488888888888816161616161616161616161624242424242424242424242424242424
order122223444468812124444666888121212242424248812121212242424242424448812121212242424242222444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ5111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1111-1111-1-1-1-1-111-1-1
χ6111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-11-1-1-111111-1-111
χ7111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1111111-1111-11-1-1-1-1-1-111
χ8111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-11-1-1-11-1111111-1-1
χ911111111111-1-1111111111-1-1-1111-1-1-1-1-1-11111-1-1-1-1-1-11-11-111-1-111-1-1111-1-1-11-111-1-1-1-111
χ1011111111111-1-1111111111-1-1-1111-1-1-1-1-1-11111-1-1-1-1-1-11-11-111-1-111-1-1-1-1-1111-11-1-11111-1-1
χ1111111111111-1-1111111111-1-1-1111-1-1-1-1-1-11111-1-1-1-1-1-1-11-11-1-111-1-11111-11-1-1-1111-1-111-1-1
χ1211111111111-1-1111111111-1-1-1111-1-1-1-1-1-11111-1-1-1-1-1-1-11-11-1-111-1-111-1-11-1111-1-1-111-1-111
χ1311111111111-1-111-1-1-1-1111-1-1-1111-1-1-1-111-1-1-1-11111-1-11-1-1111-1-1-1-1111111-1-111-1-111-1-1-1-1
χ1411111111111-1-111-1-1-1-1111-1-1-1111-1-1-1-111-1-1-1-11111-1-11-1-1111-1-1-1-111-1-1-1-111-1-111-1-11111
χ1511111111111-1-111-1-1-1-1111-1-1-1111-1-1-1-111-1-1-1-11111-1-1-111-1-1-11111-1-111-1-1-1-1-1-1-1-1111111
χ1611111111111-1-111-1-1-1-1111-1-1-1111-1-1-1-111-1-1-1-11111-1-1-111-1-1-11111-1-1-1-111111111-1-1-1-1-1-1
χ1722222-12222-122-1-12222-1-1-1222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000000000
χ1822222-12222-122-1-12222-1-1-1222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000000000
χ1922222-12222-122-1-1-2-2-2-2-1-1-1222-1-1-1-1-1-1-1-2-211111111-1-122-2-2-1-1-1-111110000000000000000
χ2022222-12222-122-1-1-2-2-2-2-1-1-1222-1-1-1-1-1-1-1-2-211111111-1-1-2-2221111-1-1-1-10000000000000000
χ2122222-12222-1-2-2-1-12222-1-1-1-2-2-2-1-1-11111-2-2-1-1-1-11111112-22-2-1-111-1-1110000000000000000
χ2222222-12222-1-2-2-1-12222-1-1-1-2-2-2-1-1-11111-2-2-1-1-1-1111111-22-2211-1-111-1-10000000000000000
χ2322222-12222-1-2-2-1-1-2-2-2-2-1-1-1-2-2-2-1-1-11111221111-1-1-1-1112-2-22-1-11111-1-10000000000000000
χ2422222-12222-1-2-2-1-1-2-2-2-2-1-1-1-2-2-2-1-1-11111221111-1-1-1-111-222-211-1-1-1-1110000000000000000
χ25222-2-222-2-22222-2-200002-2-22-2-222-222-2-200000000002-2000000000000000000002i−2i2i−2i0000
χ26222-2-222-2-22222-2-200002-2-22-2-222-222-2-200000000002-200000000000000000000−2i2i−2i2i0000
χ27222-2-222-2-222-2-2-2-200002-2-2-22222-2-2-2220000000000-22000000000000000000002i−2i−2i2i0000
χ28222-2-222-2-222-2-2-2-200002-2-2-22222-2-2-2220000000000-2200000000000000000000−2i2i2i−2i0000
χ29222-2-22-222-2200222i2i−2i−2i2-2-2000-2-220000002i2i−2i−2i0000000000000000000002000-200002i−2i00
χ30222-2-22-222-2200222i2i−2i−2i2-2-2000-2-220000002i2i−2i−2i000000000000000000000-200020000−2i2i00
χ31222-2-22-222-220022−2i−2i2i2i2-2-2000-2-22000000−2i−2i2i2i0000000000000000000002000-20000−2i2i00
χ32222-2-22-222-220022−2i−2i2i2i2-2-2000-2-22000000−2i−2i2i2i000000000000000000000-2000200002i−2i00
χ3322-22-2222-2-2200222i−2i2i−2i-2-220002-2-20000002i−2i2i−2i000000000000000000002000-200000002i−2i
χ3422-22-2222-2-2200222i−2i2i−2i-2-220002-2-20000002i−2i2i−2i00000000000000000000-200020000000−2i2i
χ3522-22-2222-2-220022−2i2i−2i2i-2-220002-2-2000000−2i2i−2i2i000000000000000000002000-20000000−2i2i
χ3622-22-2222-2-220022−2i2i−2i2i-2-220002-2-2000000−2i2i−2i2i00000000000000000000-2000200000002i−2i
χ3722-22-22-2-222222-2-20000-2-22-22-2-22222-2-20000000000-220000000000002-2002-20000000000
χ3822-22-22-2-222222-2-20000-2-22-22-2-22222-2-20000000000-22000000000000-2200-220000000000
χ3922-22-22-2-2222-2-2-2-20000-2-222-22-222-2-22200000000002-20000000000002-200-220000000000
χ4022-22-22-2-2222-2-2-2-20000-2-222-22-222-2-22200000000002-2000000000000-22002-20000000000
χ4122-2-222-22-22222222-2-22-22-2-2-22-22-222222-22-2-2222-2-2-2-20000000000000000000000000000
χ4222-2-222-22-2222222-222-2-22-2-2-22-22-22222-22-222-2-2-222-2-20000000000000000000000000000
χ4322-2-222-22-222-2-2222-2-22-22-222-2-22-2-2-2-2-2-222-2-22-2-222220000000000000000000000000000
χ4422-2-222-22-222-2-222-222-2-22-222-2-22-2-2-2-2-22-2-222-222-2-2220000000000000000000000000000
χ4522-2-22-1-22-22-122-1-12-2-221-11-2-221-11-1-1-1-12-2-111-1-1-1111100003−33−33−33−30000000000000000
χ4622-2-22-1-22-22-122-1-12-2-221-11-2-221-11-1-1-1-12-2-111-1-1-111110000−33−33−33−330000000000000000
χ4722-2-22-1-22-22-122-1-1-222-21-11-2-221-11-1-1-1-1-221-1-1111-1-11100003−33−3−33−330000000000000000
χ4822-2-22-1-22-22-122-1-1-222-21-11-2-221-11-1-1-1-1-221-1-1111-1-1110000−33−333−33−30000000000000000
χ4922-2-22-1-22-22-1-2-2-1-12-2-221-1122-21-111111-22-111-111-1-1-1-100003−3−333−3−330000000000000000
χ5022-2-22-1-22-22-1-2-2-1-12-2-221-1122-21-111111-22-111-111-1-1-1-10000−333−3−333−30000000000000000
χ5122-2-22-1-22-22-1-2-2-1-1-222-21-1122-21-1111112-21-1-11-1-111-1-100003−3−33−333−30000000000000000
χ5222-2-22-1-22-22-1-2-2-1-1-222-21-1122-21-1111112-21-1-11-1-111-1-10000−333−33−3−330000000000000000
χ53444444-4-4-4-4400-4-40000444000-4-4-400000000000000000000000000000000000000000000
χ5444444-2-4-4-4-4-200220000-2-2-2000222000000000023−2323−23000000000000000000000000000000
χ5544444-2-4-4-4-4-200220000-2-2-20002220000000000−2323−2323000000000000000000000000000000
χ56444-4-4-24-4-44-244220000-2224-4-4-2-22-2-2220000000000-220000000000000000000000000000
χ57444-4-4-24-4-44-2-4-4220000-222-444-2-2222-2-200000000002-20000000000000000000000000000
χ58444-4-4-2-444-4-200-2-24i4i−4i−4i-22200022-2000000−2i−2i2i2i0000000000000000000000000000000000
χ59444-4-4-2-444-4-200-2-2−4i−4i4i4i-22200022-20000002i2i−2i−2i0000000000000000000000000000000000
χ6044-44-4-244-4-4-200-2-24i−4i4i−4i22-2000-222000000−2i2i−2i2i0000000000000000000000000000000000
χ6144-44-4-244-4-4-200-2-2−4i4i−4i4i22-2000-2220000002i−2i2i−2i0000000000000000000000000000000000
χ6244-44-4-2-4-444-24422000022-2-44-42-2-2-2-22200000000002-20000000000000000000000000000
χ6344-44-4-2-4-444-2-4-422000022-24-442-2-222-2-20000000000-220000000000000000000000000000
χ6444-4-4444-44-4400-4-40000-44-40004-4400000000000000000000000000000000000000000000
χ6544-4-44-24-44-4-2002200002-22000-22-2000000000023−23−2323000000000000000000000000000000
χ6644-4-44-24-44-4-2002200002-22000-22-20000000000−232323−23000000000000000000000000000000
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).