Finite Group Databasebeta

← Group #136642

Character table — Group #136642

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order122222224444444444448888888822444444888888888888161616161616161616161616161616162244444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-11111-1-1-1-1
χ91111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1ii−i−iii−i−i
χ101111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111−i−iii−i−iii
χ111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1−i−iii−i−iii
χ121111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111ii−i−iii−i−i
χ131111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii11-1-111-1-1ii−i−i−i−iii
χ141111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-111-1-111−i−iiiii−i−i
χ151111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i11-1-111-1-1−i−iiiii−i−i
χ161111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-111-1-111ii−i−i−i−iii
χ1722222222222222222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000
χ1822222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222222200000000000000000000000000000000
χ192222222222-2-2-2-2-2-222-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ202222222222-2-2-2-2-2-222-2-222222222-2-2-2-22222-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ2122222222-2-222-2-2-2-2-2-2220000000022-2-222-2-200000000000022−2−222−2−222−2−222−2−20000000000000000
χ2222222222-2-222-2-2-2-2-2-2220000000022-2-222-2-2000000000000−2−222−2−222−2−222−2−2220000000000000000
χ2322222222-2-222-2-2-2-2-2-22200000000-2-222-2-22200000000000022−2−222−2−2−2−222−2−2220000000000000000
χ2422222222-2-222-2-2-2-2-2-22200000000-2-222-2-222000000000000−2−222−2−22222−2−222−2−20000000000000000
χ2522222222-2-2-2-22222-2-2-2-20000000022-2-2-2-222000000000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ2622222222-2-2-2-22222-2-2-2-20000000022-2-2-2-222000000000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ2722222222-2-2-2-22222-2-2-2-200000000-2-22222-2-2000000000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ2822222222-2-2-2-22222-2-2-2-200000000-2-22222-2-2000000000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ2922-22-22-2-22-22i−2i2i2i−2i−2i2-22i−2i000000000000000000002i2i−2i−2i22-2-21+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ3022-22-22-2-22-22i−2i2i2i−2i−2i2-22i−2i000000000000000000002i2i−2i−2i22-2-2−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ3122-22-22-2-22-22i−2i2i2i−2i−2i2-22i−2i00000000000000000000−2i−2i2i2i-2-2221+i−1−i1+i−1−i1−i−1+i1−i−1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ3222-22-22-2-22-22i−2i2i2i−2i−2i2-22i−2i00000000000000000000−2i−2i2i2i-2-222−1−i1+i−1−i1+i−1+i1−i−1+i1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ3322-22-22-2-22-2−2i2i−2i−2i2i2i2-2−2i2i000000000000000000002i2i−2i−2i-2-2221−i−1+i1−i−1+i1+i−1−i1+i−1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ3422-22-22-2-22-2−2i2i−2i−2i2i2i2-2−2i2i000000000000000000002i2i−2i−2i-2-222−1+i1−i−1+i1−i−1−i1+i−1−i1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ3522-22-22-2-22-2−2i2i−2i−2i2i2i2-2−2i2i00000000000000000000−2i−2i2i2i22-2-21−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ3622-22-22-2-22-2−2i2i−2i−2i2i2i2-2−2i2i00000000000000000000−2i−2i2i2i22-2-2−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ3722-22-22-2-2-222i−2i−2i−2i2i2i-222i−2i2i2i2i2i−2i−2i−2i−2i0000000022-2-200000000000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ0000000000000000
χ3822-22-22-2-2-222i−2i−2i−2i2i2i-222i−2i2i2i2i2i−2i−2i−2i−2i0000000022-2-20000000000000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ0000000000000000
χ3922-22-22-2-2-222i−2i−2i−2i2i2i-222i−2i−2i−2i−2i−2i2i2i2i2i00000000-2-222000000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ3000000000000000000000000
χ4022-22-22-2-2-222i−2i−2i−2i2i2i-222i−2i−2i−2i−2i−2i2i2i2i2i00000000-2-22200000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ3000000000000000000000000
χ4122-22-22-2-2-22−2i2i2i2i−2i−2i-22−2i2i2i2i2i2i−2i−2i−2i−2i00000000-2-222000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ000000000000000000000000
χ4222-22-22-2-2-22−2i2i2i2i−2i−2i-22−2i2i2i2i2i2i−2i−2i−2i−2i00000000-2-22200000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ000000000000000000000000
χ4322-22-22-2-2-22−2i2i2i2i−2i−2i-22−2i2i−2i−2i−2i−2i2i2i2i2i0000000022-2-200000000000000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ30000000000000000
χ4422-22-22-2-2-22−2i2i2i2i−2i−2i-22−2i2i−2i−2i−2i−2i2i2i2i2i0000000022-2-20000000000000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ30000000000000000
χ452-222-2-22-22-22i−2i2i−2i2i−2i-22−2i2i2i2i−2i−2i2i2i−2i−2i000000002-22-2000000000000000000000000002-22i−2i0000000000
χ462-222-2-22-22-22i−2i2i−2i2i−2i-22−2i2i2i2i−2i−2i2i2i−2i−2i000000002-22-200000000000000000000000000-22−2i2i0000000000
χ472-222-2-22-22-22i−2i2i−2i2i−2i-22−2i2i−2i−2i2i2i−2i−2i2i2i00000000-22-220000000000000000000000002-200002i−2i00000000
χ482-222-2-22-22-22i−2i2i−2i2i−2i-22−2i2i−2i−2i2i2i−2i−2i2i2i00000000-22-22000000000000000000000000-220000−2i2i00000000
χ492-222-2-22-22-2−2i2i−2i2i−2i2i-222i−2i2i2i−2i−2i2i2i−2i−2i00000000-22-220000000000000000000000002-20000−2i2i00000000
χ502-222-2-22-22-2−2i2i−2i2i−2i2i-222i−2i2i2i−2i−2i2i2i−2i−2i00000000-22-22000000000000000000000000-2200002i−2i00000000
χ512-222-2-22-22-2−2i2i−2i2i−2i2i-222i−2i−2i−2i2i2i−2i−2i2i2i000000002-22-2000000000000000000000000002-2−2i2i0000000000
χ522-222-2-22-22-2−2i2i−2i2i−2i2i-222i−2i−2i−2i2i2i−2i−2i2i2i000000002-22-200000000000000000000000000-222i−2i0000000000
χ532-2-222-2-22-2-222-222-222-2-222-2-2-2-222000000002-2-22000000000000000000000000000000002i−2i2i−2i0000
χ542-2-222-2-22-2-222-222-222-2-222-2-2-2-222000000002-2-2200000000000000000000000000000000−2i2i−2i2i0000
χ552-2-222-2-22-2-222-222-222-2-2-2-22222-2-200000000-222-20000000000000000000000000000000000002i−2i2i−2i
χ562-2-222-2-22-2-222-222-222-2-2-2-22222-2-200000000-222-2000000000000000000000000000000000000−2i2i−2i2i
χ572-2-222-2-22-2-2-2-22-2-22222222-2-2-2-22200000000-222-20000000000000000000000000000000000002-2-22
χ582-2-222-2-22-2-2-2-22-2-22222222-2-2-2-22200000000-222-2000000000000000000000000000000000000-222-2
χ592-2-222-2-22-2-2-2-22-2-222222-2-22222-2-2000000002-2-22000000000000000000000000000000002-2-220000
χ602-2-222-2-22-2-2-2-22-2-222222-2-22222-2-2000000002-2-2200000000000000000000000000000000-222-20000
χ61444-4-4-4-4400000000000022−2222−2222−2222−2200004i−4i0000002i2−2i22i2−2i2000000000000000000000000000000000000
χ62444-4-4-4-4400000000000022−2222−2222−2222−220000−4i4i000000−2i22i2−2i22i2000000000000000000000000000000000000
χ63444-4-4-4-44000000000000−2222−2222−2222−222200004i−4i000000−2i22i2−2i22i2000000000000000000000000000000000000
χ64444-4-4-4-44000000000000−2222−2222−2222−22220000−4i4i0000002i2−2i22i2−2i2000000000000000000000000000000000000
χ6544-4-44-44-40000000000002i2−2i22i2−2i2−2i22i2−2i22i20000004i−4i000022−22−2222000000000000000000000000000000000000
χ6644-4-44-44-40000000000002i2−2i22i2−2i2−2i22i2−2i22i2000000−4i4i0000−222222−22000000000000000000000000000000000000
χ6744-4-44-44-4000000000000−2i22i2−2i22i22i2−2i22i2−2i20000004i−4i0000−222222−22000000000000000000000000000000000000
χ6844-4-44-44-4000000000000−2i22i2−2i22i22i2−2i22i2−2i2000000−4i4i000022−22−2222000000000000000000000000000000000000
χ694-444-4-44-4-444i−4i−4i4i−4i4i4-4−4i4i000000000000000000000000000000000000000000000000000000000000
χ704-444-4-44-4-44−4i4i4i−4i4i−4i4-44i−4i000000000000000000000000000000000000000000000000000000000000
χ714-44-444-4-40000000000002i2−2i2−2i22i22i2−2i2−2i22i2004i−4i00000000000022−2222−2200000000000000000000000000000000
χ724-44-444-4-40000000000002i2−2i2−2i22i22i2−2i2−2i22i200−4i4i000000000000−2222−222200000000000000000000000000000000
χ734-44-444-4-4000000000000−2i22i22i2−2i2−2i22i22i2−2i2004i−4i000000000000−2222−222200000000000000000000000000000000
χ744-44-444-4-4000000000000−2i22i22i2−2i2−2i22i22i2−2i200−4i4i00000000000022−2222−2200000000000000000000000000000000
χ754-4-444-4-4444444-4-44-4-4-4-4000000000000000000000000000000000000000000000000000000000000
χ764-4-444-4-4444-4-4-444-4-4-444000000000000000000000000000000000000000000000000000000000000
χ774-4-4-4-444400000000000022−22−2222−222222−224-40000000000000022−22−222200000000000000000000000000000000
χ784-4-4-4-444400000000000022−22−2222−222222−22-4400000000000000−222222−2200000000000000000000000000000000
χ794-4-4-4-4444000000000000−222222−2222−22−22224-400000000000000−222222−2200000000000000000000000000000000
χ804-4-4-4-4444000000000000−222222−2222−22−2222-440000000000000022−22−222200000000000000000000000000000000

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