Finite Group Databasebeta

← Group #112428

Character table — Group #112428

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111122222222222222222244444488888888888888888888888816161616161616161616161616161616
order12222244444444444444442244444444444488888888888888882444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ51111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ9111111-1-11111-1-111-1-1-1-1-1-1-1-1111-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i1-11-111-1-1ii−i−iii−i−i
χ10111111-1-11111-1-111-1-1-1-1-1-1-1-1111-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i-11-11-1-111−i−iii−i−iii
χ11111111-1-11111-1-111-1-1-1-1-1-1-1-1111-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii1-11-1-1-111ii−i−i−i−iii
χ12111111-1-11111-1-111-1-1-1-1-1-1-1-1111-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii-11-1111-1-1−i−iiiii−i−i
χ13111111-1-11111-1-111-1-1-1-1-1-1-1-1111-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii1-11-111-1-1−i−iii−i−iii
χ14111111-1-11111-1-111-1-1-1-1-1-1-1-1111-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii-11-11-1-111ii−i−iii−i−i
χ15111111-1-11111-1-111-1-1-1-1-1-1-1-1111-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i1-11-1-1-111−i−iiiii−i−i
χ16111111-1-11111-1-111-1-1-1-1-1-1-1-1111-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i-11-1111-1-1ii−i−i−i−iii
χ17222222222222-2-2-2-2222222-2-2-2-2-2-2000000000000000022-2-222-2-20000000000000000
χ18222222222222-2-2-2-2222222-2-2-2-2-2-20000000000000000-2-222-2-2220000000000000000
χ1922222222-2-2-2-222-2-222-2-2-2-2-2-2-22220000000000000000000000000000000000002i−2i2i−2i
χ2022222222-2-2-2-222-2-222-2-2-2-2-2-2-2222000000000000000000000000000000000000−2i2i−2i2i
χ2122222222-2-2-2-2-2-22222-2-2-2-2222-2-2-20000000000000000000000002-2-22000000000000
χ2222222222-2-2-2-2-2-22222-2-2-2-2222-2-2-2000000000000000000000000-222-2000000000000
χ23222222-2-2222222-2-2-2-2-2-2-2-222-2-2-2200000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ24222222-2-2222222-2-2-2-2-2-2-2-222-2-2-220000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ25222222-2-2-2-2-2-22222-2-22222-2-22-2-2200000000000000000000000022-2-2000000000000
χ26222222-2-2-2-2-2-22222-2-22222-2-22-2-22000000000000000000000000-2-222000000000000
χ27222222-2-2-2-2-2-2-2-2-2-2-2-2222222-222-20000000000000000000000000000000000002-2-22
χ28222222-2-2-2-2-2-2-2-2-2-2-2-2222222-222-2000000000000000000000000000000000000-222-2
χ292222-2-22222-2-22222-2-222-2-2-22-22-2-20000000022-2-222-2-2000000000000000000000000
χ302222-2-22222-2-22222-2-222-2-2-22-22-2-200000000-2-222-2-222000000000000000000000000
χ312222-2-22222-2-2-2-2-2-2-2-222-2-22-22-2222i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000
χ322222-2-22222-2-2-2-2-2-2-2-222-2-22-22-222−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000
χ332222-2-222-2-22222-2-2-2-2-2-2222-222-2-2000000000000000000000000000000002i−2i2i−2i0000
χ342222-2-222-2-22222-2-2-2-2-2-2222-222-2-200000000000000000000000000000000−2i2i−2i2i0000
χ352222-2-222-2-222-2-222-2-2-2-222-22-2-22200000000000000000000000000002-22-200000000
χ362222-2-222-2-222-2-222-2-2-2-222-22-2-2220000000000000000000000000000-22-2200000000
χ372222-2-2-2-222-2-222-2-222-2-222-222-22-222-2-2-2-22200000000000000000000000000000000
χ382222-2-2-2-222-2-222-2-222-2-222-222-22-2-2-22222-2-200000000000000000000000000000000
χ392222-2-2-2-222-2-2-2-22222-2-2222-2-22-220000000022-2-2-2-222000000000000000000000000
χ402222-2-2-2-222-2-2-2-22222-2-2222-2-22-2200000000-2-22222-2-2000000000000000000000000
χ412222-2-2-2-2-2-22222222222-2-22-2-2-22-200000000000000000000000000002-2-2200000000
χ422222-2-2-2-2-2-22222222222-2-22-2-2-22-20000000000000000000000000000-222-200000000
χ432222-2-2-2-2-2-222-2-2-2-22222-2-2-2222-22000000000000000000000000000000002-2-220000
χ442222-2-2-2-2-2-222-2-2-2-22222-2-2-2222-2200000000000000000000000000000000-222-20000
χ452-22-22-22i−2i2-22-200002i−2i2i−2i2i−2i0000001+i−1−i1+i−1−i1−i−1+i1−i−1+ii2−i2i2−i22−22−2002ζ3−2ζ3002ζ−2ζ0000000000000000
χ462-22-22-22i−2i2-22-200002i−2i2i−2i2i−2i0000001+i−1−i1+i−1−i1−i−1+i1−i−1+i−i2i2−i2i2−22−2200−2ζ32ζ300−2ζ2ζ0000000000000000
χ472-22-22-22i−2i2-22-200002i−2i2i−2i2i−2i000000−1−i1+i−1−i1+i−1+i1−i−1+i1−ii2−i2i2−i22−22−200−2ζ32ζ300−2ζ2ζ0000000000000000
χ482-22-22-22i−2i2-22-200002i−2i2i−2i2i−2i000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i−i2i2−i2i2−22−22002ζ3−2ζ3002ζ−2ζ0000000000000000
χ492-22-22-2−2i2i2-22-20000−2i2i−2i2i−2i2i0000001−i−1+i1−i−1+i1+i−1−i1+i−1−ii2−i2i2−i2−22−22002ζ−2ζ002ζ3−2ζ30000000000000000
χ502-22-22-2−2i2i2-22-20000−2i2i−2i2i−2i2i0000001−i−1+i1−i−1+i1+i−1−i1+i−1−i−i2i2−i2i22−22−200−2ζ2ζ00−2ζ32ζ30000000000000000
χ512-22-22-2−2i2i2-22-20000−2i2i−2i2i−2i2i000000−1+i1−i−1+i1−i−1−i1+i−1−i1+ii2−i2i2−i2−22−2200−2ζ2ζ00−2ζ32ζ30000000000000000
χ522-22-22-2−2i2i2-22-20000−2i2i−2i2i−2i2i000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i−i2i2−i2i22−22−2002ζ−2ζ002ζ3−2ζ30000000000000000
χ532-22-2-222i−2i2-2-220000−2i2i2i−2i−2i2i0000001−i−1+i−1+i1−i−1−i1+i1+i−1−ii2−i2−i2i22−2−222ζ−2ζ002ζ3−2ζ3000000000000000000
χ542-22-2-222i−2i2-2-220000−2i2i2i−2i−2i2i0000001−i−1+i−1+i1−i−1−i1+i1+i−1−i−i2i2i2−i2−222−2−2ζ2ζ00−2ζ32ζ3000000000000000000
χ552-22-2-222i−2i2-2-220000−2i2i2i−2i−2i2i000000−1+i1−i1−i−1+i1+i−1−i−1−i1+ii2−i2−i2i22−2−22−2ζ2ζ00−2ζ32ζ3000000000000000000
χ562-22-2-222i−2i2-2-220000−2i2i2i−2i−2i2i000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i−i2i2i2−i2−222−22ζ−2ζ002ζ3−2ζ3000000000000000000
χ572-22-2-22−2i2i2-2-2200002i−2i−2i2i2i−2i0000001+i−1−i−1−i1+i−1+i1−i1−i−1+ii2−i2−i2i2−222−22ζ3−2ζ3002ζ−2ζ000000000000000000
χ582-22-2-22−2i2i2-2-2200002i−2i−2i2i2i−2i0000001+i−1−i−1−i1+i−1+i1−i1−i−1+i−i2i2i2−i22−2−22−2ζ32ζ300−2ζ2ζ000000000000000000
χ592-22-2-22−2i2i2-2-2200002i−2i−2i2i2i−2i000000−1−i1+i1+i−1−i1−i−1+i−1+i1−ii2−i2−i2i2−222−2−2ζ32ζ300−2ζ2ζ000000000000000000
χ602-22-2-22−2i2i2-2-2200002i−2i−2i2i2i−2i000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i−i2i2i2−i22−2−222ζ3−2ζ3002ζ−2ζ000000000000000000
χ614-44-44-44i−4i-44-4400004i−4i−4i4i−4i4i0000000000000000000000000000000000000000000000
χ624-44-44-4−4i4i-44-440000−4i4i4i−4i4i−4i0000000000000000000000000000000000000000000000
χ634-44-4-444i−4i-444-40000−4i4i−4i4i4i−4i0000000000000000000000000000000000000000000000
χ644-44-4-44−4i4i-444-400004i−4i4i−4i−4i4i0000000000000000000000000000000000000000000000
χ6588-8-800000000008-80000000000000000000000000000000000000000000000000000
χ6688-8-80000000000-880000000000000000000000000000000000000000000000000000
χ678-8-88000000008i−8i000000000000000000000000000000000000000000000000000000
χ688-8-8800000000−8i8i000000000000000000000000000000000000000000000000000000

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