Finite Group Databasebeta

← Group #7253

Character table — Group #7253

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46
size1111111122224444444488888888888888888888888888
order1222444422442244444444888888888888888888888888
χ11111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ6111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ7111111111111-1-1-1-1-1-1-1-111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ8111111111111-1-1-1-1-1-1-1-111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ91111-1-1-1-111-1-111-1-1-111-11-1ii−i−iii−i−i11-1-111-1-1ii−i−iii−i−i
χ101111-1-1-1-111-1-111-1-1-111-11-1ii−i−iii−i−i-1-111-1-111−i−iii−i−iii
χ111111-1-1-1-111-1-111-1-1-111-11-1−i−iii−i−iii11-1-111-1-1−i−iii−i−iii
χ121111-1-1-1-111-1-111-1-1-111-11-1−i−iii−i−iii-1-111-1-111ii−i−iii−i−i
χ131111-1-1-1-111-1-1-1-1111-1-111-1ii−i−i−i−iiiii−i−i−i−iii-1-11111-1-1
χ141111-1-1-1-111-1-1-1-1111-1-111-1ii−i−i−i−iii−i−iiiii−i−i11-1-1-1-111
χ151111-1-1-1-111-1-1-1-1111-1-111-1−i−iiiii−i−iii−i−i−i−iii11-1-1-1-111
χ161111-1-1-1-111-1-1-1-1111-1-111-1−i−iiiii−i−i−i−iiiii−i−i-1-11111-1-1
χ17222222222222222-2-2-2-22-2-2000000000000000000000000
χ18222222222222-2-2-22222-2-2-2000000000000000000000000
χ192222-2-2-2-222-2-222-222-2-2-2-22000000000000000000000000
χ202222-2-2-2-222-2-2-2-22-2-2222-22000000000000000000000000
χ2122-2-222-2-22-22-22-220000-200000000002−22−22−22−200000000
χ2222-2-222-2-22-22-22-220000-20000000000−22−22−22−2200000000
χ2322-2-222-2-22-22-2-22-2000020000000000i2−i2i2−i2−i2i2−i2i200000000
χ2422-2-222-2-22-22-2-22-2000020000000000−i2i2−i2i2i2−i2i2−i200000000
χ2522-2-222-2-2-22-220002i−2i2i−2i00000000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i
χ2622-2-222-2-2-22-220002i−2i2i−2i0000000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i
χ2722-2-222-2-2-22-22000−2i2i−2i2i00000000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i
χ2822-2-222-2-2-22-22000−2i2i−2i2i0000000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i
χ2922-2-2-2-2222-2-222-2-20000200000000002−2−222−2−2200000000
χ3022-2-2-2-2222-2-222-2-2000020000000000−222−2−222−200000000
χ3122-2-2-2-2222-2-22-2220000-20000000000i2−i2−i2i2−i2i2i2−i200000000
χ3222-2-2-2-2222-2-22-2220000-20000000000−i2i2i2−i2i2−i2−i2i200000000
χ3322-2-2-2-222-222-20002i−2i−2i2i00000000000000000001−i−1+i−1+i1−i−1−i1+i1+i−1−i
χ3422-2-2-2-222-222-20002i−2i−2i2i0000000000000000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i
χ3522-2-2-2-222-222-2000−2i2i2i−2i00000000000000000001+i−1−i−1−i1+i−1+i1−i1−i−1+i
χ3622-2-2-2-222-222-2000−2i2i2i−2i0000000000000000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i
χ3744444444-4-4-4-40000000000000000000000000000000000
χ384444-4-4-4-4-4-4440000000000000000000000000000000000
χ394-44-44i−4i4i−4i000000000000002ζ−2ζ2ζ3−2ζ300000000000000000000
χ404-44-44i−4i4i−4i00000000000000−2ζ2ζ−2ζ32ζ300000000000000000000
χ414-44-4−4i4i−4i4i000000000000002ζ3−2ζ32ζ−2ζ00000000000000000000
χ424-44-4−4i4i−4i4i00000000000000−2ζ32ζ3−2ζ2ζ00000000000000000000
χ434-4-444i−4i−4i4i0000000000000000002ζ3−2ζ32ζ−2ζ0000000000000000
χ444-4-444i−4i−4i4i000000000000000000−2ζ32ζ3−2ζ2ζ0000000000000000
χ454-4-44−4i4i4i−4i0000000000000000002ζ−2ζ2ζ3−2ζ30000000000000000
χ464-4-44−4i4i4i−4i000000000000000000−2ζ2ζ−2ζ32ζ30000000000000000

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