Finite Group Databasebeta

← Group #150415

Character table — Group #150415

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11112222224444444444888888888888888888888161616161616323232323232
order124424444422244444444888888888888888888882488884816161616
χ111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1
χ311111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ411111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11111
χ51111111111-1-11-1-1-1-11-1-1111iiiiiiii−i−i−i−i−i−i−i−i-1-111111-1-1-1ii−i−i
χ61111111111-1-11-1-1-1-11-1-1111iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1-1-11-111−i−iii
χ71111111111-1-11-1-1-1-11-1-1111−i−i−i−i−i−i−i−iiiiiiiii-1-111111-1-1-1−i−iii
χ81111111111-1-11-1-1-1-11-1-1111−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1-1-11-111ii−i−i
χ911111-1-1-1-11111-1-1-1-1111-1-1-11111-1-1-1-11111-1-1-1-11111-1-11-11-11-11-1
χ1011111-1-1-1-11111-1-1-1-1111-1-1-11111-1-1-1-11111-1-1-1-111-1-1111-1-11-11-11
χ1111111-1-1-1-11111-1-1-1-1111-1-1-1-1-1-1-11111-1-1-1-111111111-1-11-11-1-11-11
χ1211111-1-1-1-11111-1-1-1-1111-1-1-1-1-1-1-11111-1-1-1-1111111-1-1111-1-111-11-1
χ1311111-1-1-1-11-1-1111111-1-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii-1-111-1-111-11i−i−ii
χ1411111-1-1-1-11-1-1111111-1-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii-1-1-1-111111-1−iii−i
χ1511111-1-1-1-11-1-1111111-1-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-111-1-111-11−iii−i
χ1611111-1-1-1-11-1-1111111-1-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-111111-1i−i−ii
χ17222222222222222222222-2-20000000000000000-2-20000-2-2000000
χ182222222222-2-22-2-2-2-22-2-22-2-20000000000000000220000-22000000
χ1922222-2-2-2-22222-2-2-2-2222-2220000000000000000-2-20000-22000000
χ2022222-2-2-2-22-2-2222222-2-2-2220000000000000000220000-2-2000000
χ2122-2-220000-200-222-2-220002i−2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i2i−2i000000000000
χ2222-2-220000-200-222-2-220002i−2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i2i−2i000000000000
χ2322-2-220000-200-222-2-22000−2i2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i−2i2i000000000000
χ2422-2-220000-200-222-2-22000−2i2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−2i2i000000000000
χ2522-2-220000-200-2-2-22220002i−2i1−i1−i−1+i−1+i−1−i−1−i1+i1+i1+i1+i−1−i−1−i−1+i−1+i1−i1−i−2i2i000000000000
χ2622-2-220000-200-2-2-22220002i−2i−1+i−1+i1−i1−i1+i1+i−1−i−1−i−1−i−1−i1+i1+i1−i1−i−1+i−1+i−2i2i000000000000
χ2722-2-220000-200-2-2-2222000−2i2i1+i1+i−1−i−1−i−1+i−1+i1−i1−i1−i1−i−1+i−1+i−1−i−1−i1+i1+i2i−2i000000000000
χ2822-2-220000-200-2-2-2222000−2i2i−1−i−1−i1+i1+i1−i1−i−1+i−1+i−1+i−1+i1−i1−i1+i1+i−1−i−1−i2i−2i000000000000
χ29444444444400-40000-400-400000000000000000000000000000000
χ3044444-4-4-4-4400-40000-400400000000000000000000000000000000
χ3144-4-440000-44440000-4-4-4000000000000000000000000000000000
χ3244-4-440000-4-4-440000-444000000000000000000000000000000000
χ3344-4-4-44i4i−4i−4i400000000000000000000000000000002-22i−2i00000000
χ3444-4-4-44i4i−4i−4i40000000000000000000000000000000-22−2i2i00000000
χ3544-4-4-4−4i−4i4i4i400000000000000000000000000000002-2−2i2i00000000
χ3644-4-4-4−4i−4i4i4i40000000000000000000000000000000-222i−2i00000000
χ374-44i−4i02+2i−2−2i2−2i−2+2i02-202-22i−2i02i−2i000i2−i22−2i2−i22−2i2−i22−2i2−i22−200000000000000
χ384-44i−4i02+2i−2−2i2−2i−2+2i02-202-22i−2i02i−2i000−i2i2−22−i2i2−22−i2i2−22−i2i2−2200000000000000
χ394-44i−4i02+2i−2−2i2−2i−2+2i0-220-22−2i2i0−2i2i0002−2−i2i22−2−i2i2−22i2−i2−22i2−i200000000000000
χ404-44i−4i02+2i−2−2i2−2i−2+2i0-220-22−2i2i0−2i2i000−22i2−i2−22i2−i22−2−i2i22−2−i2i200000000000000
χ414-44i−4i0−2−2i2+2i−2+2i2−2i02-20-22−2i2i02i−2i000i2−i22−2−i2i2−22i2−i22−2−i2i2−2200000000000000
χ424-44i−4i0−2−2i2+2i−2+2i2−2i02-20-22−2i2i02i−2i000−i2i2−22i2−i22−2−i2i2−22i2−i22−200000000000000
χ434-44i−4i0−2−2i2+2i−2+2i2−2i0-2202-22i−2i0−2i2i0002−2−i2i2−22i2−i2−22i2−i22−2−i2i200000000000000
χ444-44i−4i0−2−2i2+2i−2+2i2−2i0-2202-22i−2i0−2i2i000−22i2−i22−2−i2i22−2−i2i2−22i2−i200000000000000
χ454-4−4i4i02−2i−2+2i2+2i−2−2i02-202-2−2i2i0−2i2i000i2−i2−22i2−i2−22i2−i2−22i2−i2−2200000000000000
χ464-4−4i4i02−2i−2+2i2+2i−2−2i02-202-2−2i2i0−2i2i000−i2i22−2−i2i22−2−i2i22−2−i2i22−200000000000000
χ474-4−4i4i02−2i−2+2i2+2i−2−2i0-220-222i−2i02i−2i0002−2i2−i22−2i2−i2−22−i2i2−22−i2i200000000000000
χ484-4−4i4i02−2i−2+2i2+2i−2−2i0-220-222i−2i02i−2i000−22−i2i2−22−i2i22−2i2−i22−2i2−i200000000000000
χ494-4−4i4i0−2+2i2−2i−2−2i2+2i02-20-222i−2i0−2i2i000i2−i2−22−i2i22−2i2−i2−22−i2i22−200000000000000
χ504-4−4i4i0−2+2i2−2i−2−2i2+2i02-20-222i−2i0−2i2i000−i2i22−2i2−i2−22−i2i22−2i2−i2−2200000000000000
χ514-4−4i4i0−2+2i2−2i−2−2i2+2i0-2202-2−2i2i02i−2i0002−2i2−i2−22−i2i2−22−i2i22−2i2−i200000000000000
χ524-4−4i4i0−2+2i2−2i−2−2i2+2i0-2202-2−2i2i02i−2i000−22−i2i22−2i2−i22−2i2−i2−22−i2i200000000000000
χ538888-80000-80000000000000000000000000000000000000000000

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