Finite Group Databasebeta

← Group #152913

Character table — Group #152913

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11112222224444444444888888888888888888888161616161616323232323232
order12442488882444448888224488888888888888888224488888888
χ111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111
χ511111111111-1-1-1-11-1-1-1-11-11-11iiiiiiii−i−i−i−i−i−i−i−i11111-1-1-1ii−i−i
χ611111111111-1-1-1-11-1-1-1-11-11-11iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11-111−i−iii
χ711111111111-1-1-1-11-1-1-1-11-11-11−i−i−i−i−i−i−i−iiiiiiiii11111-1-1-1−i−iii
χ811111111111-1-1-1-11-1-1-1-11-11-11−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11-111ii−i−i
χ9111111-1-1-1-1111111-1-1-1-11111-11111-1-1-1-11111-1-1-1-11-11-1-1-11-11-11-1
χ10111111-1-1-1-1111111-1-1-1-11111-11111-1-1-1-11111-1-1-1-1-11-11-1-1-11-11-11
χ11111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-11111-1-1-1-111111-11-1-1-11-1-11-11
χ12111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-11111-1-1-1-11111-11-11-1-1-111-11-1
χ13111111-1-1-1-11-1-1-1-1111111-11-1-1iiii−i−i−i−i−i−i−i−iiiii1-11-1-11-11i−i−ii
χ14111111-1-1-1-11-1-1-1-1111111-11-1-1iiii−i−i−i−i−i−i−i−iiiii-11-11-111-1−iii−i
χ15111111-1-1-1-11-1-1-1-1111111-11-1-1−i−i−i−iiiiiiiii−i−i−i−i1-11-1-11-11−iii−i
χ16111111-1-1-1-11-1-1-1-1111111-11-1-1−i−i−i−iiiiiiiii−i−i−i−i-11-11-111-1i−i−ii
χ1722222222222222222222-2-2-2-2200000000000000000000-2-2000000
χ1822222222222-2-2-2-22-2-2-2-2-22-22200000000000000000000-22000000
χ19222222-2-2-2-2222222-2-2-2-2-2-2-2-2-20000000000000000000022000000
χ20222222-2-2-2-22-2-2-2-222222-22-22-2000000000000000000002-2000000
χ2122-2-22-20000-222-2-22000022-2-2000002i2i−2i−2i00002i2i−2i−2i000000000000
χ2222-2-22-20000-222-2-22000022-2-200000−2i−2i2i2i0000−2i−2i2i2i000000000000
χ2322-2-22-20000-222-2-220000-2-222022-2-2000022-2-20000000000000000
χ2422-2-22-20000-222-2-220000-2-2220-2-2220000-2-2220000000000000000
χ2522-2-22-20000-2-2-222200002-2-220000022-2-20000-2-222000000000000
χ2622-2-22-20000-2-2-222200002-2-2200000-2-222000022-2-2000000000000
χ2722-2-22-20000-2-2-22220000-222-202i2i−2i−2i0000−2i−2i2i2i0000000000000000
χ2822-2-22-20000-2-2-22220000-222-20−2i−2i2i2i00002i2i−2i−2i0000000000000000
χ294444444444-40000-400000000-40000000000000000000000000000
χ30444444-4-4-4-4-40000-40000000040000000000000000000000000000
χ3144-4-44-4000040000-44i4i−4i−4i000000000000000000000000000000000
χ3244-4-44-4000040000-4−4i−4i4i4i000000000000000000000000000000000
χ3344-4-4-4444-4-4000000000000000000000000000000022-2-200000000
χ3444-4-4-4444-4-40000000000000000000000000000000-2-22200000000
χ3544-4-4-44-4-44400000000000000000000000000000002-2-2200000000
χ3644-4-4-44-4-4440000000000000000000000000000000-222-200000000
χ374-44i−4i0022−222i2−2i202-22i−2i02ζ−2ζ2ζ3−2ζ300000i2−i22−21+i−1−i1−i−1+ii2−i22−21+i−1−i1−i−1+i000000000000
χ384-44i−4i0022−222i2−2i202-22i−2i02ζ−2ζ2ζ3−2ζ300000−i2i2−22−1−i1+i−1+i1−i−i2i2−22−1−i1+i−1+i1−i000000000000
χ394-44i−4i0022−222i2−2i20-22−2i2i0−2ζ2ζ−2ζ32ζ3000002−2−i2i21−i−1+i−1−i1+i−22i2−i2−1+i1−i1+i−1−i000000000000
χ404-44i−4i0022−222i2−2i20-22−2i2i0−2ζ2ζ−2ζ32ζ300000−22i2−i2−1+i1−i1+i−1−i2−2−i2i21−i−1+i−1−i1+i000000000000
χ414-44i−4i00−2222−2i22i202-22i−2i0−2ζ2ζ−2ζ32ζ300000i2−i22−2−1−i1+i−1+i1−ii2−i22−2−1−i1+i−1+i1−i000000000000
χ424-44i−4i00−2222−2i22i202-22i−2i0−2ζ2ζ−2ζ32ζ300000−i2i2−221+i−1−i1−i−1+i−i2i2−221+i−1−i1−i−1+i000000000000
χ434-44i−4i00−2222−2i22i20-22−2i2i02ζ−2ζ2ζ3−2ζ3000002−2−i2i2−1+i1−i1+i−1−i−22i2−i21−i−1+i−1−i1+i000000000000
χ444-44i−4i00−2222−2i22i20-22−2i2i02ζ−2ζ2ζ3−2ζ300000−22i2−i21−i−1+i−1−i1+i2−2−i2i2−1+i1−i1+i−1−i000000000000
χ454-4−4i4i0022−22−2i22i202-2−2i2i0−2ζ32ζ3−2ζ2ζ00000i2−i2−22−1+i1−i−1−i1+ii2−i2−22−1+i1−i−1−i1+i000000000000
χ464-4−4i4i0022−22−2i22i202-2−2i2i0−2ζ32ζ3−2ζ2ζ00000−i2i22−21−i−1+i1+i−1−i−i2i22−21−i−1+i1+i−1−i000000000000
χ474-4−4i4i0022−22−2i22i20-222i−2i02ζ3−2ζ32ζ−2ζ000002−2i2−i21+i−1−i−1+i1−i−22−i2i2−1−i1+i1−i−1+i000000000000
χ484-4−4i4i0022−22−2i22i20-222i−2i02ζ3−2ζ32ζ−2ζ00000−22−i2i2−1−i1+i1−i−1+i2−2i2−i21+i−1−i−1+i1−i000000000000
χ494-4−4i4i00−22222i2−2i202-2−2i2i02ζ3−2ζ32ζ−2ζ00000i2−i2−221−i−1+i1+i−1−ii2−i2−221−i−1+i1+i−1−i000000000000
χ504-4−4i4i00−22222i2−2i202-2−2i2i02ζ3−2ζ32ζ−2ζ00000−i2i22−2−1+i1−i−1−i1+i−i2i22−2−1+i1−i−1−i1+i000000000000
χ514-4−4i4i00−22222i2−2i20-222i−2i0−2ζ32ζ3−2ζ2ζ000002−2i2−i2−1−i1+i1−i−1+i−22−i2i21+i−1−i−1+i1−i000000000000
χ524-4−4i4i00−22222i2−2i20-222i−2i0−2ζ32ζ3−2ζ2ζ00000−22−i2i21+i−1−i−1+i1−i2−2i2−i2−1−i1+i1−i−1+i000000000000
χ538888-8-800000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.