Finite Group Databasebeta

← Group #146713

Character table — Group #146713

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222224444444444444444444444444444444488888888888816161616161616161616161616161616
order12224444224488888888222222444444444444448888888888882244888888884444444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111-1-1-1-111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ61111111111111111111111-1-1-1-111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ71111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ81111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ9111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1
χ10111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111
χ11111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111-1-111
χ12111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111-1-111-1-1
χ13111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111ii−i−i−i−iiiii−i−i−i−iii
χ14111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−iiiii−i−i−i−iiiii−i−i
χ15111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1ii−i−i−i−iii−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1−i−iiiii−i−iii−i−i−i−iii
χ171-1-1111-1-1-111-1iiii−i−i−i−i1-111-1-11-111-1-11111-1-1-1-1iiii−i−i−i−iii−i−i1-11-1ii−i−iii−i−i1-1i−i1-1i−i1-1i−i1-1i−i
χ181-1-1111-1-1-111-1iiii−i−i−i−i1-111-1-11-111-1-11111-1-1-1-1iiii−i−i−i−iii−i−i1-11-1ii−i−iii−i−i-11−ii-11−ii-11−ii-11−ii
χ191-1-1111-1-1-111-1iiii−i−i−i−i1-111-1-11-111-1-1-1-1-1-11111−i−i−i−iiiiiii−i−i-11-11ii−i−i−i−iii1-1i−i1-1i−i-11−ii-11−ii
χ201-1-1111-1-1-111-1iiii−i−i−i−i1-111-1-11-111-1-1-1-1-1-11111−i−i−i−iiiiiii−i−i-11-11ii−i−i−i−iii-11−ii-11−ii1-1i−i1-1i−i
χ211-1-1111-1-1-111-1iiii−i−i−i−i1-1-1-1111-1-1-1111111-1-1-1-1iiii−i−i−i−iii−i−i-11-11−i−iii−i−iiii−i-11−ii1-1i−i-11−ii1-1
χ221-1-1111-1-1-111-1iiii−i−i−i−i1-1-1-1111-1-1-1111111-1-1-1-1iiii−i−i−i−iii−i−i-11-11−i−iii−i−iii−ii1-1i−i-11−ii1-1i−i-11
χ231-1-1111-1-1-111-1iiii−i−i−i−i1-1-1-1111-1-1-111-1-1-1-11111−i−i−i−iiiiiii−i−i1-11-1−i−iiiii−i−ii−i-11−ii1-1−ii1-1i−i-11
χ241-1-1111-1-1-111-1iiii−i−i−i−i1-1-1-1111-1-1-111-1-1-1-11111−i−i−i−iiiiiii−i−i1-11-1−i−iiiii−i−i−ii1-1i−i-11i−i-11−ii1-1
χ251-1-1111-1-1-111-1−i−i−i−iiiii1-111-1-11-111-1-11111-1-1-1-1−i−i−i−iiiii−i−iii1-11-1−i−iii−i−iii1-1−ii1-1−ii1-1−ii1-1−ii
χ261-1-1111-1-1-111-1−i−i−i−iiiii1-111-1-11-111-1-11111-1-1-1-1−i−i−i−iiiii−i−iii1-11-1−i−iii−i−iii-11i−i-11i−i-11i−i-11i−i
χ271-1-1111-1-1-111-1−i−i−i−iiiii1-111-1-11-111-1-1-1-1-1-11111iiii−i−i−i−i−i−iii-11-11−i−iiiii−i−i1-1−ii1-1−ii-11i−i-11i−i
χ281-1-1111-1-1-111-1−i−i−i−iiiii1-111-1-11-111-1-1-1-1-1-11111iiii−i−i−i−i−i−iii-11-11−i−iiiii−i−i-11i−i-11i−i1-1−ii1-1−ii
χ291-1-1111-1-1-111-1−i−i−i−iiiii1-1-1-1111-1-1-1111111-1-1-1-1−i−i−i−iiiii−i−iii-11-11ii−i−iii−i−ii−i1-1−ii-11i−i1-1−ii-11
χ301-1-1111-1-1-111-1−i−i−i−iiiii1-1-1-1111-1-1-1111111-1-1-1-1−i−i−i−iiiii−i−iii-11-11ii−i−iii−i−i−ii-11i−i1-1−ii-11i−i1-1
χ311-1-1111-1-1-111-1−i−i−i−iiiii1-1-1-1111-1-1-111-1-1-1-11111iiii−i−i−i−i−i−iii1-11-1ii−i−i−i−iiii−i1-1−ii-11−ii-11i−i1-1
χ321-1-1111-1-1-111-1−i−i−i−iiiii1-1-1-1111-1-1-111-1-1-1-11111iiii−i−i−i−i−i−iii1-11-1ii−i−i−i−iii−ii-11i−i1-1i−i1-1−ii-11
χ3322222222222222222222-2-22-22-2-2-22-22-20000000000000000-2-2-2-200002-22-200000000000000000000
χ3422222222222222222222-2-2-22-22-2-2-22-220000000000000000-2-2-2-20000-22-2200000000000000000000
χ35222222222222-2-2-2-2-2-2-2-2-2-22-22-2-2-22-22-2000000000000000022220000-22-2200000000000000000000
χ36222222222222-2-2-2-2-2-2-2-2-2-2-22-22-2-2-22-220000000000000000222200002-22-200000000000000000000
χ372222-2-2-2-222-2-200000000222-22-2-2-2-22-22000000002i2i−2i−2i2i2i−2i−2i0000000000002i−2i2i−2i0000000000000000
χ382222-2-2-2-222-2-200000000222-22-2-2-2-22-2200000000−2i−2i2i2i−2i−2i2i2i000000000000−2i2i−2i2i0000000000000000
χ392222-2-2-2-222-2-20000000022-22-22-2-22-22-2000000002i2i−2i−2i2i2i−2i−2i000000000000−2i2i−2i2i0000000000000000
χ402222-2-2-2-222-2-20000000022-22-22-2-22-22-200000000−2i−2i2i2i−2i−2i2i2i0000000000002i−2i2i−2i0000000000000000
χ412222-2-2-2-222-2-200000000-2-2222222-2-2-2-222-2-222-2-200000000000022-2-2000000000000000000000000
χ422222-2-2-2-222-2-200000000-2-2222222-2-2-2-2-2-222-2-222000000000000-2-222000000000000000000000000
χ432222-2-2-2-222-2-200000000-2-2-2-2-2-222222222-2-222-2-2000000000000-2-222000000000000000000000000
χ442222-2-2-2-222-2-200000000-2-2-2-2-2-2222222-2-222-2-22200000000000022-2-2000000000000000000000000
χ452-2-2222-2-2-222-22i2i2i2i−2i−2i−2i−2i-222-2-22-222-2-220000000000000000−2i−2i2i2i00002i−2i−2i2i00000000000000000000
χ462-2-2222-2-2-222-22i2i2i2i−2i−2i−2i−2i-22-222-2-22-222-20000000000000000−2i−2i2i2i0000−2i2i2i−2i00000000000000000000
χ472-2-2222-2-2-222-2−2i−2i−2i−2i2i2i2i2i-222-2-22-222-2-2200000000000000002i2i−2i−2i0000−2i2i2i−2i00000000000000000000
χ482-2-2222-2-2-222-2−2i−2i−2i−2i2i2i2i2i-22-222-2-22-222-200000000000000002i2i−2i−2i00002i−2i−2i2i00000000000000000000
χ492-2-22-2-222-22-22000000002-22-2-22-22-222-20000000022-2-2-2-2220000000000002-2-220000000000000000
χ502-2-22-2-222-22-22000000002-22-2-22-22-222-200000000-2-22222-2-2000000000000-222-20000000000000000
χ512-2-22-2-222-22-22000000002-2-222-2-222-2-220000000022-2-2-2-222000000000000-222-20000000000000000
χ522-2-22-2-222-22-22000000002-2-222-2-222-2-2200000000-2-22222-2-20000000000002-2-220000000000000000
χ532-2-22-2-222-22-2200000000-2222-2-22-2-2-22222-2-2-2-2220000000000002-2-22000000000000000000000000
χ542-2-22-2-222-22-2200000000-2222-2-22-2-2-222-2-22222-2-2000000000000-222-2000000000000000000000000
χ552-2-22-2-222-22-2200000000-22-2-2222-222-2-222-2-2-2-222000000000000-222-2000000000000000000000000
χ562-2-22-2-222-22-2200000000-22-2-2222-222-2-2-2-22222-2-20000000000002-2-22000000000000000000000000
χ5744444444-4-4-4-40000000000000000000000000000000000004i−4i4i−4i0000000000000000000000000000
χ5844444444-4-4-4-4000000000000000000000000000000000000−4i4i−4i4i0000000000000000000000000000
χ594444-4-4-4-4-4-44444-4-444-4-4000000000000000000000000000000000000000000000000000000000000
χ604444-4-4-4-4-4-444-4-444-4-444000000000000000000000000000000000000000000000000000000000000
χ6144-4-44i−4i4i−4i00002i2−2i222−222i2−2i222−220000000000002-22i−2i2-22i−2i2ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ300000000000000000000000000000000
χ6244-4-44i−4i4i−4i00002i2−2i222−222i2−2i222−22000000000000-22−2i2i-22−2i2i−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ300000000000000000000000000000000
χ6344-4-44i−4i4i−4i0000−2i22i2−2222−2i22i2−22220000000000002-22i−2i2-22i−2i−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ300000000000000000000000000000000
χ6444-4-44i−4i4i−4i0000−2i22i2−2222−2i22i2−2222000000000000-22−2i2i-22−2i2i2ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ300000000000000000000000000000000
χ6544-4-4−4i4i−4i4i00002i2−2i2−22222i2−2i2−22220000000000002-2−2i2i2-2−2i2i2ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ00000000000000000000000000000000
χ6644-4-4−4i4i−4i4i00002i2−2i2−22222i2−2i2−2222000000000000-222i−2i-222i−2i−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ00000000000000000000000000000000
χ6744-4-4−4i4i−4i4i0000−2i22i222−22−2i22i222−220000000000002-2−2i2i2-2−2i2i−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ00000000000000000000000000000000
χ6844-4-4−4i4i−4i4i0000−2i22i222−22−2i22i222−22000000000000-222i−2i-222i−2i2ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ00000000000000000000000000000000
χ694-44-44i−4i−4i4i000022−22−2i22i2−22222i2−2i20000000000002-22i−2i-22−2i2i−2ζ32ζ32ζ−2ζ2ζ3−2ζ3−2ζ2ζ00000000000000000000000000000000
χ704-44-44i−4i−4i4i000022−22−2i22i2−22222i2−2i2000000000000-22−2i2i2-22i−2i2ζ3−2ζ3−2ζ2ζ−2ζ32ζ32ζ−2ζ00000000000000000000000000000000
χ714-44-44i−4i−4i4i0000−22222i2−2i222−22−2i22i20000000000002-22i−2i-22−2i2i2ζ3−2ζ3−2ζ2ζ−2ζ32ζ32ζ−2ζ00000000000000000000000000000000
χ724-44-44i−4i−4i4i0000−22222i2−2i222−22−2i22i2000000000000-22−2i2i2-22i−2i−2ζ32ζ32ζ−2ζ2ζ3−2ζ3−2ζ2ζ00000000000000000000000000000000
χ734-44-4−4i4i4i−4i000022−222i2−2i2−2222−2i22i20000000000002-2−2i2i-222i−2i2ζ−2ζ−2ζ32ζ3−2ζ2ζ2ζ3−2ζ300000000000000000000000000000000
χ744-44-4−4i4i4i−4i000022−222i2−2i2−2222−2i22i2000000000000-222i−2i2-2−2i2i−2ζ2ζ2ζ3−2ζ32ζ−2ζ−2ζ32ζ300000000000000000000000000000000
χ754-44-4−4i4i4i−4i0000−2222−2i22i222−222i2−2i20000000000002-2−2i2i-222i−2i−2ζ2ζ2ζ3−2ζ32ζ−2ζ−2ζ32ζ300000000000000000000000000000000
χ764-44-4−4i4i4i−4i0000−2222−2i22i222−222i2−2i2000000000000-222i−2i2-2−2i2i2ζ−2ζ−2ζ32ζ3−2ζ2ζ2ζ3−2ζ300000000000000000000000000000000
χ774-4-4444-4-44-4-440000000000000000000000000000000000004-4-440000000000000000000000000000
χ784-4-4444-4-44-4-44000000000000000000000000000000000000-444-40000000000000000000000000000
χ794-4-44-4-4444-44-44i4i−4i−4i−4i−4i4i4i000000000000000000000000000000000000000000000000000000000000
χ804-4-44-4-4444-44-4−4i−4i4i4i4i4i−4i−4i000000000000000000000000000000000000000000000000000000000000

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