Finite Group Databasebeta

← Group #128233

Character table — Group #128233

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222224444444444444444444444444444444488888888888816161616161616161616161616161616
order122244442244444444444444444488888888888888888888888888888888888816161616161616161616161616161616
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i
χ911111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-111-1-111-1-111-1-1
χ1011111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-111
χ1111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii
χ1211111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1ii−i−i−i−iii−i−iiiii−i−i
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1−i−iiiii−i−iii−i−i−i−iii
χ1711111111-1-11111-1-1-1-1-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i1111-1-1-1-1ii−i−i11-1-1ii−i−i1-1i−i1-1i−i1-1i−i1-1i−i
χ1811111111-1-11111-1-1-1-1-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i1111-1-1-1-1ii−i−i11-1-1ii−i−i-11−ii-11−ii-11−ii-11−ii
χ1911111111-1-11111-1-1-1-1-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i-1-1-1-11111−i−iii-1-111−i−iiii−i-11i−i-11−ii1-1−ii1-1
χ2011111111-1-11111-1-1-1-1-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i-1-1-1-11111−i−iii-1-111−i−iii−ii1-1−ii1-1i−i-11i−i-11
χ2111111111-1-11111-1-1-1-1-1-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii1111-1-1-1-1ii−i−i-1-111−i−iii1-1i−i-11−ii1-1i−i-11−ii
χ2211111111-1-11111-1-1-1-1-1-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii1111-1-1-1-1ii−i−i-1-111−i−iii-11−ii1-1i−i-11−ii1-1i−i
χ2311111111-1-11111-1-1-1-1-1-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii-1-1-1-11111−i−iii11-1-1ii−i−ii−i-11−ii1-1−ii1-1i−i-11
χ2411111111-1-11111-1-1-1-1-1-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii-1-1-1-11111−i−iii11-1-1ii−i−i−ii1-1i−i-11i−i-11−ii1-1
χ2511111111-1-11111-1-1-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−iii11-1-1−i−iii1-1−ii1-1−ii1-1−ii1-1−ii
χ2611111111-1-11111-1-1-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−iii11-1-1−i−iii-11i−i-11i−i-11i−i-11i−i
χ2711111111-1-11111-1-1-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii-1-1-1-11111ii−i−i-1-111ii−i−ii−i1-1i−i1-1−ii-11−ii-11
χ2811111111-1-11111-1-1-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii-1-1-1-11111ii−i−i-1-111ii−i−i−ii-11−ii-11i−i1-1i−i1-1
χ2911111111-1-11111-1-1-1-1-1-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i1111-1-1-1-1−i−iii-1-111ii−i−i1-1−ii-11i−i1-1−ii-11i−i
χ3011111111-1-11111-1-1-1-1-1-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i1111-1-1-1-1−i−iii-1-111ii−i−i-11i−i1-1−ii-11i−i1-1−ii
χ3111111111-1-11111-1-1-1-1-1-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i-1-1-1-11111ii−i−i11-1-1−i−iiii−i1-1−ii-11−ii-11i−i1-1
χ3211111111-1-11111-1-1-1-1-1-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i-1-1-1-11111ii−i−i11-1-1−i−iii−ii-11i−i1-1i−i1-1−ii-11
χ332222222222-2-2-2-222-2-2-2-2000000002i2i−2i−2i2i2i−2i−2i0000000022-2-222-2-200002i−2i2i−2i00000000000000000000
χ342222222222-2-2-2-222-2-2-2-2000000002i2i−2i−2i2i2i−2i−2i00000000-2-222-2-2220000−2i2i−2i2i00000000000000000000
χ352222222222-2-2-2-222-2-2-2-200000000−2i−2i2i2i−2i−2i2i2i0000000022-2-222-2-20000−2i2i−2i2i00000000000000000000
χ362222222222-2-2-2-222-2-2-2-200000000−2i−2i2i2i−2i−2i2i2i00000000-2-222-2-22200002i−2i2i−2i00000000000000000000
χ3722222222-2-2-2-2-2-2-2-22222000000002i2i−2i−2i−2i−2i2i2i0000000022-2-2-2-22200002i−2i−2i2i00000000000000000000
χ3822222222-2-2-2-2-2-2-2-22222000000002i2i−2i−2i−2i−2i2i2i00000000-2-22222-2-20000−2i2i2i−2i00000000000000000000
χ3922222222-2-2-2-2-2-2-2-2222200000000−2i−2i2i2i2i2i−2i−2i0000000022-2-2-2-2220000−2i2i2i−2i00000000000000000000
χ4022222222-2-2-2-2-2-2-2-2222200000000−2i−2i2i2i2i2i−2i−2i00000000-2-22222-2-200002i−2i−2i2i00000000000000000000
χ412222-2-2-2-22222-2-2-2-222-2-2000000000000000022-2-222-2-22i−2i2i−2i2i−2i2i−2i000000002i−2i2i−2i0000000000000000
χ422222-2-2-2-22222-2-2-2-222-2-2000000000000000022-2-222-2-2−2i2i−2i2i−2i2i−2i2i00000000−2i2i−2i2i0000000000000000
χ432222-2-2-2-22222-2-2-2-222-2-20000000000000000-2-222-2-2222i−2i2i−2i2i−2i2i−2i00000000−2i2i−2i2i0000000000000000
χ442222-2-2-2-22222-2-2-2-222-2-20000000000000000-2-222-2-222−2i2i−2i2i−2i2i−2i2i000000002i−2i2i−2i0000000000000000
χ452222-2-2-2-222-2-222-2-2-2-22222-2-222-2-200000000000000002i−2i−2i2i2i−2i−2i2i2i−2i2i−2i000000000000000000000000
χ462222-2-2-2-222-2-222-2-2-2-22222-2-222-2-20000000000000000−2i2i2i−2i−2i2i2i−2i−2i2i−2i2i000000000000000000000000
χ472222-2-2-2-222-2-222-2-2-2-222-2-222-2-22200000000000000002i−2i−2i2i2i−2i−2i2i−2i2i−2i2i000000000000000000000000
χ482222-2-2-2-222-2-222-2-2-2-222-2-222-2-2220000000000000000−2i2i2i−2i−2i2i2i−2i2i−2i2i−2i000000000000000000000000
χ492222-2-2-2-2-2-222-2-222-2-22200000000000000002i2i−2i−2i−2i−2i2i2i2i−2i2i−2i−2i2i−2i2i00000000-222-20000000000000000
χ502222-2-2-2-2-2-222-2-222-2-22200000000000000002i2i−2i−2i−2i−2i2i2i−2i2i−2i2i2i−2i2i−2i000000002-2-220000000000000000
χ512222-2-2-2-2-2-222-2-222-2-2220000000000000000−2i−2i2i2i2i2i−2i−2i2i−2i2i−2i−2i2i−2i2i000000002-2-220000000000000000
χ522222-2-2-2-2-2-222-2-222-2-2220000000000000000−2i−2i2i2i2i2i−2i−2i−2i2i−2i2i2i−2i2i−2i00000000-222-20000000000000000
χ532222-2-2-2-2-2-2-2-2222222-2-22i2i−2i−2i−2i−2i2i2i00000000000000002i−2i−2i2i−2i2i2i−2i-222-2000000000000000000000000
χ542222-2-2-2-2-2-2-2-2222222-2-22i2i−2i−2i−2i−2i2i2i0000000000000000−2i2i2i−2i2i−2i−2i2i2-2-22000000000000000000000000
χ552222-2-2-2-2-2-2-2-2222222-2-2−2i−2i2i2i2i2i−2i−2i00000000000000002i−2i−2i2i−2i2i2i−2i2-2-22000000000000000000000000
χ562222-2-2-2-2-2-2-2-2222222-2-2−2i−2i2i2i2i2i−2i−2i0000000000000000−2i2i2i−2i2i−2i−2i2i-222-2000000000000000000000000
χ5744-4-444-4-4004i−4i4i−4i0000000000000000004ζ−4ζ4ζ3−4ζ300000000000000000000000000000000000000000000
χ5844-4-444-4-4004i−4i4i−4i000000000000000000−4ζ4ζ−4ζ34ζ300000000000000000000000000000000000000000000
χ5944-4-444-4-400−4i4i−4i4i0000000000000000004ζ3−4ζ34ζ−4ζ00000000000000000000000000000000000000000000
χ6044-4-444-4-400−4i4i−4i4i000000000000000000−4ζ34ζ3−4ζ4ζ00000000000000000000000000000000000000000000
χ6144-4-4-4-444004i−4i−4i4i000000000000004ζ−4ζ4ζ3−4ζ3000000000000000000000000000000000000000000000000
χ6244-4-4-4-444004i−4i−4i4i00000000000000−4ζ4ζ−4ζ34ζ3000000000000000000000000000000000000000000000000
χ6344-4-4-4-44400−4i4i4i−4i000000000000004ζ3−4ζ34ζ−4ζ000000000000000000000000000000000000000000000000
χ6444-4-4-4-44400−4i4i4i−4i00000000000000−4ζ34ζ3−4ζ4ζ000000000000000000000000000000000000000000000000
χ654-44-44i−4i4i−4i000000004-44i−4i2+2i−2−2i2−2i−2+2i2−2i−2+2i2+2i−2−2i0000000000000000000000000000000000000000000000000000
χ664-44-44i−4i4i−4i000000004-44i−4i−2−2i2+2i−2+2i2−2i−2+2i2−2i−2−2i2+2i0000000000000000000000000000000000000000000000000000
χ674-44-44i−4i4i−4i00000000-44−4i4i2−2i−2+2i−2−2i2+2i2+2i−2−2i−2+2i2−2i0000000000000000000000000000000000000000000000000000
χ684-44-44i−4i4i−4i00000000-44−4i4i−2+2i2−2i2+2i−2−2i−2−2i2+2i2−2i−2+2i0000000000000000000000000000000000000000000000000000
χ694-44-4−4i4i−4i4i000000004-4−4i4i2−2i−2+2i2+2i−2−2i2+2i−2−2i2−2i−2+2i0000000000000000000000000000000000000000000000000000
χ704-44-4−4i4i−4i4i000000004-4−4i4i−2+2i2−2i−2−2i2+2i−2−2i2+2i−2+2i2−2i0000000000000000000000000000000000000000000000000000
χ714-44-4−4i4i−4i4i00000000-444i−4i2+2i−2−2i−2+2i2−2i2−2i−2+2i−2−2i2+2i0000000000000000000000000000000000000000000000000000
χ724-44-4−4i4i−4i4i00000000-444i−4i−2−2i2+2i2−2i−2+2i−2+2i2−2i2+2i−2−2i0000000000000000000000000000000000000000000000000000
χ734-4-444i−4i−4i4i4-400004i−4i000000000000000000002i2−2i222−222i2−2i222−22000000000000000000000000000000000000
χ744-4-444i−4i−4i4i4-400004i−4i00000000000000000000−2i22i2−2222−2i22i2−2222000000000000000000000000000000000000
χ754-4-444i−4i−4i4i-440000−4i4i0000000000000000000022−22−2i22i2−22222i2−2i2000000000000000000000000000000000000
χ764-4-444i−4i−4i4i-440000−4i4i00000000000000000000−22222i2−2i222−22−2i22i2000000000000000000000000000000000000
χ774-4-44−4i4i4i−4i4-40000−4i4i000000000000000000002i2−2i2−22222i2−2i2−2222000000000000000000000000000000000000
χ784-4-44−4i4i4i−4i4-40000−4i4i00000000000000000000−2i22i222−22−2i22i222−22000000000000000000000000000000000000
χ794-4-44−4i4i4i−4i-4400004i−4i0000000000000000000022−222i2−2i2−2222−2i22i2000000000000000000000000000000000000
χ804-4-44−4i4i4i−4i-4400004i−4i00000000000000000000−2222−2i22i222−222i2−2i2000000000000000000000000000000000000

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