Finite Group Databasebeta

← Group #152692

Character table — Group #152692

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11112222224444444444888888888888888888888161616161616323232323232
order12442444442224444444224448888888888888888244488444888
χ111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-11-1-1
χ41111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-111
χ51111111111-1-11-1-1-1-11-1-11-111-1iiiiiiii−i−i−i−i−i−i−i−i111-111-1i−i-1i−i
χ61111111111-1-11-1-1-1-11-1-11-111-1iiiiiiii−i−i−i−i−i−i−i−i-1-11-1-1-11−ii1−ii
χ71111111111-1-11-1-1-1-11-1-11-111-1−i−i−i−i−i−i−i−iiiiiiiii111-111-1−ii-1−ii
χ81111111111-1-11-1-1-1-11-1-11-111-1−i−i−i−i−i−i−i−iiiiiiiii-1-11-1-1-11i−i1i−i
χ9111111-1-1-1-111111-1-11-1-11-11-1-1iiii−i−i−i−iiiii−i−i−i−i11-11-1-11i−i-1−ii
χ10111111-1-1-1-111111-1-11-1-11-11-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1111-1−ii1i−i
χ11111111-1-1-1-111111-1-11-1-11-11-1-1−i−i−i−iiiii−i−i−i−iiiii11-11-1-11−ii-1i−i
χ12111111-1-1-1-111111-1-11-1-11-11-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1111-1i−i1−ii
χ13111111-1-1-1-1-1-11-1-111111111-111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1111-1-1
χ14111111-1-1-1-1-1-11-1-111111111-111111-1-1-1-1-1-1-1-11111-1-1-1-1111-1-1-111
χ15111111-1-1-1-1-1-11-1-111111111-11-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1111
χ16111111-1-1-1-1-1-11-1-111111111-11-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-1-1
χ1722222222222222222222-2-2-22-2000000000000000000-2-200000000
χ182222222222-2-22-2-2-2-22-2-2-22-222000000000000000000-2200000000
χ19222222-2-2-2-222222-2-22-2-2-22-2-220000000000000000002-200000000
χ20222222-2-2-2-2-2-22-2-222222-2-2-2-2-20000000000000000002200000000
χ2122-2-22-2000000-200222-2-22-2-2022i2i−2i−2i000000002i2i−2i−2i000000000000
χ2222-2-22-2000000-200222-2-22-2-202−2i−2i2i2i00000000−2i−2i2i2i000000000000
χ2322-2-22-2000000-200222-2-2-2220-200002i2i−2i−2i2i2i−2i−2i0000000000000000
χ2422-2-22-2000000-200222-2-2-2220-20000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ2522-2-22-2000000-200-2-222222-20-222-2-200000000-2-222000000000000
χ2622-2-22-2000000-200-2-222222-20-2-2-2220000000022-2-2000000000000
χ2722-2-22-2000000-200-2-2222-2-2202000022-2-2-2-2220000000000000000
χ2822-2-22-2000000-200-2-2222-2-22020000-2-22222-2-20000000000000000
χ29444444444400-40000-400000-400000000000000000000000000000
χ30444444-4-4-4-400-40000-400000400000000000000000000000000000
χ3144-4-44-40000444-4-400-400000000000000000000000000000000000
χ3244-4-44-40000-4-444400-400000000000000000000000000000000000
χ3344-4-4-444i4i−4i−4i00000000000000000000000000000002-2002i−2i000000
χ3444-4-4-444i4i−4i−4i0000000000000000000000000000000-2200−2i2i000000
χ3544-4-4-44−4i−4i4i4i00000000000000000000000000000002-200−2i2i000000
χ3644-4-4-44−4i−4i4i4i0000000000000000000000000000000-22002i−2i000000
χ374-44i−4i002+2i−2−2i2−2i−2+2i2-202i−2i2i−2i02-200000i2−i22−2i2−i22−22−2i2−i22−2i2−i2000000000000
χ384-44i−4i002+2i−2−2i2−2i−2+2i2-202i−2i2i−2i02-200000−i2i2−22−i2i2−22−22−i2i2−22−i2i2000000000000
χ394-44i−4i002+2i−2−2i2−2i−2+2i-220−2i2i−2i2i0-22000002−2−i2i22−2−i2i2i2−i2−22i2−i2−22000000000000
χ404-44i−4i002+2i−2−2i2−2i−2+2i-220−2i2i−2i2i0-2200000−22i2−i2−22i2−i2−i2i22−2−i2i22−2000000000000
χ414-44i−4i00−2−2i2+2i−2+2i2−2i2-202i−2i−2i2i0-22000002−2−i2i2−22i2−i2−i2i22−2i2−i2−22000000000000
χ424-44i−4i00−2−2i2+2i−2+2i2−2i2-202i−2i−2i2i0-2200000−22i2−i22−2−i2i2i2−i2−22−i2i22−2000000000000
χ434-44i−4i00−2−2i2+2i−2+2i2−2i-220−2i2i2i−2i02-200000i2−i22−2−i2i2−22−22−i2i22−2i2−i2000000000000
χ444-44i−4i00−2−2i2+2i−2+2i2−2i-220−2i2i2i−2i02-200000−i2i2−22i2−i22−22−2i2−i2−22−i2i2000000000000
χ454-4−4i4i002−2i−2+2i2+2i−2−2i2-20−2i2i−2i2i02-200000i2−i2−22i2−i2−22−22i2−i2−22i2−i2000000000000
χ464-4−4i4i002−2i−2+2i2+2i−2−2i2-20−2i2i−2i2i02-200000−i2i22−2−i2i22−22−2−i2i22−2−i2i2000000000000
χ474-4−4i4i002−2i−2+2i2+2i−2−2i-2202i−2i2i−2i0-22000002−2i2−i22−2i2−i2−i2i2−22−i2i2−22000000000000
χ484-4−4i4i002−2i−2+2i2+2i−2−2i-2202i−2i2i−2i0-2200000−22−i2i2−22−i2i2i2−i22−2i2−i22−2000000000000
χ494-4−4i4i00−2+2i2−2i−2−2i2+2i2-20−2i2i2i−2i0-22000002−2i2−i2−22−i2i2i2−i22−2−i2i2−22000000000000
χ504-4−4i4i00−2+2i2−2i−2−2i2+2i2-20−2i2i2i−2i0-2200000−22−i2i22−2i2−i2−i2i2−22i2−i22−2000000000000
χ514-4−4i4i00−2+2i2−2i−2−2i2+2i-2202i−2i−2i2i02-200000i2−i2−22−i2i22−22−2−i2i2−22i2−i2000000000000
χ524-4−4i4i00−2+2i2−2i−2−2i2+2i-2202i−2i−2i2i02-200000−i2i22−2i2−i2−22−22i2−i22−2−i2i2000000000000
χ538888-8-800000000000000000000000000000000000000000000000

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