Finite Group Databasebeta

← Group #137653

Character table — Group #137653

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order122222224444444444448888888822444444888888888888161616161616161616161616161616164444444488888888
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
χ51111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ911111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i
χ1011111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-1-111−i−iii−i−iii
χ1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii
χ1211111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111ii−i−iii−i−i
χ1311111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111ii−i−i−i−iii
χ1411111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−i
χ1511111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111−i−iiiii−i−i
χ1611111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1ii−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
χ19222222222222-2-2-2-2-2-2-2-2000000002222-2-2-2-2000000000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ20222222222222-2-2-2-2-2-2-2-2000000002222-2-2-2-2000000000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ21222222222222-2-2-2-2-2-2-2-200000000-2-2-2-22222000000000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ22222222222222-2-2-2-2-2-2-2-200000000-2-2-2-22222000000000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ2322222222-2-2-2-22222-2-2-2-22222222222-2-222-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ2422222222-2-2-2-22222-2-2-2-222222222-2-222-2-222-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-222220000000022-2-2-2-22200000000000022−2−2−2−22222−2−2−2−2220000000000000000
χ2622222222-2-2-2-2-2-2-2-222220000000022-2-2-2-222000000000000−2−22222−2−2−2−22222−2−20000000000000000
χ2722222222-2-2-2-2-2-2-2-2222200000000-2-22222-2-200000000000022−2−2−2−222−2−22222−2−20000000000000000
χ2822222222-2-2-2-2-2-2-2-2222200000000-2-22222-2-2000000000000−2−22222−2−222−2−2−2−2220000000000000000
χ2922-2-22-22-22i2i−2i−2i2-22-22i2i−2i−2i2i2i−2i−2i2i2i−2i−2i0000000022-2-20000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ
χ3022-2-22-22-22i2i−2i−2i2-22-22i2i−2i−2i2i2i−2i−2i2i2i−2i−2i0000000022-2-2000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ
χ3122-2-22-22-22i2i−2i−2i2-22-22i2i−2i−2i−2i−2i2i2i−2i−2i2i2i00000000-2-222000000000000000000000000000000002ζ3−2ζ32ζ−2ζ0000
χ3222-2-22-22-22i2i−2i−2i2-22-22i2i−2i−2i−2i−2i2i2i−2i−2i2i2i00000000-2-22200000000000000000000000000000000−2ζ32ζ3−2ζ2ζ0000
χ3322-2-22-22-2−2i−2i2i2i2-22-2−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i00000000-2-222000000000000000000000000000000002ζ−2ζ2ζ3−2ζ30000
χ3422-2-22-22-2−2i−2i2i2i2-22-2−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i00000000-2-22200000000000000000000000000000000−2ζ2ζ−2ζ32ζ30000
χ3522-2-22-22-2−2i−2i2i2i2-22-2−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i0000000022-2-20000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ3
χ3622-2-22-22-2−2i−2i2i2i2-22-2−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i0000000022-2-2000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ3
χ372-22-2-222-22i−2i2i−2i-222-22i−2i2i−2i2i2i−2i−2i−2i−2i2i2i000000002-22-200000000000000000000000000002i−2i2-200000000
χ382-22-2-222-22i−2i2i−2i-222-22i−2i2i−2i2i2i−2i−2i−2i−2i2i2i000000002-22-20000000000000000000000000000−2i2i-2200000000
χ392-22-2-222-22i−2i2i−2i-222-22i−2i2i−2i−2i−2i2i2i2i2i−2i−2i00000000-22-220000000000000000000000002i−2i2-2000000000000
χ402-22-2-222-22i−2i2i−2i-222-22i−2i2i−2i−2i−2i2i2i2i2i−2i−2i00000000-22-22000000000000000000000000−2i2i-22000000000000
χ412-22-2-222-2−2i2i−2i2i-222-2−2i2i−2i2i2i2i−2i−2i−2i−2i2i2i00000000-22-220000000000000000000000002i−2i-22000000000000
χ422-22-2-222-2−2i2i−2i2i-222-2−2i2i−2i2i2i2i−2i−2i−2i−2i2i2i00000000-22-22000000000000000000000000−2i2i2-2000000000000
χ432-22-2-222-2−2i2i−2i2i-222-2−2i2i−2i2i−2i−2i2i2i2i2i−2i−2i000000002-22-200000000000000000000000000002i−2i-2200000000
χ442-22-2-222-2−2i2i−2i2i-222-2−2i2i−2i2i−2i−2i2i2i2i2i−2i−2i000000002-22-20000000000000000000000000000−2i2i2-200000000
χ452-2-22-2-2222-2-2222-2-2-222-2000000000000000000002i2i−2i−2i2i2i−2i−2i2−22−22−22−2i2−i2i2−i2i2−i2i2−i20000000000000000
χ462-2-22-2-2222-2-2222-2-2-222-2000000000000000000002i2i−2i−2i2i2i−2i−2i−22−22−22−22−i2i2−i2i2−i2i2−i2i20000000000000000
χ472-2-22-2-2222-2-2222-2-2-222-200000000000000000000−2i−2i2i2i−2i−2i2i2i2−22−22−22−2−i2i2−i2i2−i2i2−i2i20000000000000000
χ482-2-22-2-2222-2-2222-2-2-222-200000000000000000000−2i−2i2i2i−2i−2i2i2i−22−22−22−22i2−i2i2−i2i2−i2i2−i20000000000000000
χ492-2-22-2-2222-2-22-2-2222-2-222222-2-2-2-2000000002-2-22000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ502-2-22-2-2222-2-22-2-2222-2-222222-2-2-2-2000000002-2-2200000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ512-2-22-2-2222-2-22-2-2222-2-22-2-2-2-2222200000000-222-200000000000000002-2-222-2-220000000000000000
χ522-2-22-2-2222-2-22-2-2222-2-22-2-2-2-2222200000000-222-20000000000000000-222-2-222-20000000000000000
χ532-2-22-2-222-222-222-2-22-2-22000000000000000000002i2i−2i−2i−2i−2i2i2ii2−i2i2−i2−i2i2−i2i2−22−222−22−20000000000000000
χ542-2-22-2-222-222-222-2-22-2-22000000000000000000002i2i−2i−2i−2i−2i2i2i−i2i2−i2i2i2−i2i2−i22−22−2−22−220000000000000000
χ552-2-22-2-222-222-222-2-22-2-2200000000000000000000−2i−2i2i2i2i2i−2i−2ii2−i2i2−i2−i2i2−i2i22−22−2−22−220000000000000000
χ562-2-22-2-222-222-222-2-22-2-2200000000000000000000−2i−2i2i2i2i2i−2i−2i−i2i2−i2i2i2−i2i2−i2−22−222−22−20000000000000000
χ572-2-22-2-222-222-2-2-222-222-22222-2-2-2-200000000-222-200000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ582-2-22-2-222-222-2-2-222-222-22222-2-2-2-200000000-222-20000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ592-2-22-2-222-222-2-2-222-222-2-2-2-2-22222000000002-2-22000000002-2-22-222-2000000000000000000000000
χ602-2-22-2-222-222-2-2-222-222-2-2-2-2-22222000000002-2-2200000000-222-22-2-22000000000000000000000000
χ614444-4-4-4-400000000000022−2222−2222−2222−224-40000000000000022−2222−2200000000000000000000000000000000
χ624444-4-4-4-400000000000022−2222−2222−2222−22-4400000000000000−2222−222200000000000000000000000000000000
χ634444-4-4-4-4000000000000−2222−2222−2222−22224-400000000000000−2222−222200000000000000000000000000000000
χ644444-4-4-4-4000000000000−2222−2222−2222−2222-440000000000000022−2222−2200000000000000000000000000000000
χ6544-4-44-44-44i4i−4i−4i-44-44−4i−4i4i4i000000000000000000000000000000000000000000000000000000000000
χ6644-4-44-44-4−4i−4i4i4i-44-444i4i−4i−4i000000000000000000000000000000000000000000000000000000000000
χ6744-4-4-44-440000000000002i2−2i2−2i22i22i2−2i2−2i22i20000004-400002i2−2i22i2−2i2000000000000000000000000000000000000
χ6844-4-4-44-440000000000002i2−2i2−2i22i22i2−2i2−2i22i2000000-440000−2i22i2−2i22i2000000000000000000000000000000000000
χ6944-4-4-44-44000000000000−2i22i22i2−2i2−2i22i22i2−2i20000004-40000−2i22i2−2i22i2000000000000000000000000000000000000
χ7044-4-4-44-44000000000000−2i22i22i2−2i2−2i22i22i2−2i2000000-4400002i2−2i22i2−2i2000000000000000000000000000000000000
χ714-44-44-4-440000000000002i2−2i2−2i22i2−2i22i22i2−2i2004i−4i0000000022−22−2222000000000000000000000000000000000000
χ724-44-44-4-440000000000002i2−2i2−2i22i2−2i22i22i2−2i200−4i4i00000000−222222−22000000000000000000000000000000000000
χ734-44-44-4-44000000000000−2i22i22i2−2i22i2−2i2−2i22i2004i−4i00000000−222222−22000000000000000000000000000000000000
χ744-44-44-4-44000000000000−2i22i22i2−2i22i2−2i2−2i22i200−4i4i0000000022−22−2222000000000000000000000000000000000000
χ754-44-4-444-44i−4i4i−4i4-4-44−4i4i−4i4i000000000000000000000000000000000000000000000000000000000000
χ764-44-4-444-4−4i4i−4i4i4-4-444i−4i4i−4i000000000000000000000000000000000000000000000000000000000000
χ774-4-4444-4-400000000000022−2222−22−2222−222200004i−4i00000000002i2−2i2−2i22i200000000000000000000000000000000
χ784-4-4444-4-400000000000022−2222−22−2222−22220000−4i4i0000000000−2i22i22i2−2i200000000000000000000000000000000
χ794-4-4444-4-4000000000000−2222−222222−2222−2200004i−4i0000000000−2i22i22i2−2i200000000000000000000000000000000
χ804-4-4444-4-4000000000000−2222−222222−2222−220000−4i4i00000000002i2−2i2−2i22i200000000000000000000000000000000

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