Finite Group Databasebeta

← Group #114355

Character table — Group #114355

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111122222222222222222244444488888888888888888888888816161616161616161616161616161616
order12222244444444444444442244448888888888888888888888884444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1
χ911111111-1-1111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1ii−i−iii−i−i
χ1011111111-1-1111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111−i−iii−i−iii
χ1111111111-1-1111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1−i−iii−i−iii
χ1211111111-1-1111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111ii−i−iii−i−i
χ1311111111-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111ii−i−i−i−iii
χ1411111111-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−i
χ1511111111-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111−i−iiiii−i−i
χ1611111111-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1ii−i−i−i−iii
χ172222222222-2-2-2-2-2-222-2-2-2-2222-2-2-200000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ182222222222-2-2-2-2-2-222-2-2-2-2222-2-2-20000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ1922222222-2-2-2-2-2-2-2-2-2-22222-2-22-222000000000000000022-2-2-2-2220000000000000000
χ2022222222-2-2-2-2-2-2-2-2-2-22222-2-22-2220000000000000000-2-22222-2-20000000000000000
χ21222222-2-2222222-2-2222222-2-2-2-2-2-20000000022-2-222-2-2000000000000000000000000
χ22222222-2-2222222-2-2222222-2-2-2-2-2-200000000-2-222-2-222000000000000000000000000
χ23222222-2-222-2-2-2-22222-2-2-2-2-2-2-222222-2-222-2-200000000000000000000000000000000
χ24222222-2-222-2-2-2-22222-2-2-2-2-2-2-2222-2-222-2-22200000000000000000000000000000000
χ25222222-2-2-2-22222-2-2-2-2-2-2-2-222-2-222000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ26222222-2-2-2-22222-2-2-2-2-2-2-2-222-2-22200000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ27222222-2-2-2-2-2-2-2-222-2-2222222-22-2-222-2-2-2-22200000000000000000000000000000000
χ28222222-2-2-2-2-2-2-2-222-2-2222222-22-2-2-2-22222-2-200000000000000000000000000000000
χ292222-2-2222222-2-222-2-222-2-22-2-2-2-22000000000000000000000000002-2002-200000000
χ302222-2-2222222-2-222-2-222-2-22-2-2-2-2200000000000000000000000000-2200-2200000000
χ312222-2-22222-2-222-2-2-2-2-2-2222-2-222-2000000000000000000000000000000002i−2i2i−2i0000
χ322222-2-22222-2-222-2-2-2-2-2-2222-2-222-200000000000000000000000000000000−2i2i−2i2i0000
χ332222-2-222-2-222-2-22222-2-222-22-2-22-2000000000000000000000000002-200-2200000000
χ342222-2-222-2-222-2-22222-2-222-22-2-22-200000000000000000000000000-22002-200000000
χ352222-2-222-2-2-2-222-2-22222-2-2-22-22-22000000000000000000000000000000002-2-220000
χ362222-2-222-2-2-2-222-2-22222-2-2-22-22-2200000000000000000000000000000000-222-20000
χ372222-2-2-2-22222-2-2-2-2-2-222-2-2-22222-20000000000000000000000000000000000002i−2i2i−2i
χ382222-2-2-2-22222-2-2-2-2-2-222-2-2-22222-2000000000000000000000000000000000000−2i2i−2i2i
χ392222-2-2-2-222-2-22222-2-2-2-222-222-2-220000000000000000000000002-2002-20000000000
χ402222-2-2-2-222-2-22222-2-2-2-222-222-2-22000000000000000000000000-2200-220000000000
χ412222-2-2-2-2-2-222-2-2-2-222-2-2222-222-220000000000000000000000000000000000002-2-22
χ422222-2-2-2-2-2-222-2-2-2-222-2-2222-222-22000000000000000000000000000000000000-222-2
χ432222-2-2-2-2-2-2-2-222222222-2-22-22-22-20000000000000000000000002-200-220000000000
χ442222-2-2-2-2-2-2-2-222222222-2-22-22-22-2000000000000000000000000-22002-20000000000
χ452-2-222-2002i−2i2-22-2002i−2i2i−2i2i−2i0000002−22−2i2−i2i2−i2002ζ3−2ζ3002ζ−2ζ1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ462-2-222-2002i−2i2-22-2002i−2i2i−2i2i−2i0000002−22−2i2−i2i2−i200−2ζ32ζ300−2ζ2ζ−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ472-2-222-2002i−2i2-22-2002i−2i2i−2i2i−2i000000−22−22−i2i2−i2i2002ζ3−2ζ3002ζ−2ζ−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ482-2-222-2002i−2i2-22-2002i−2i2i−2i2i−2i000000−22−22−i2i2−i2i200−2ζ32ζ300−2ζ2ζ1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ492-2-222-2002i−2i-22-22002i−2i−2i2i−2i2i0000002−2−22i2−i2−i2i22ζ−2ζ002ζ3−2ζ3001+i−1−i−1−i1+i−1+i1−i1−i−1+i0000000000000000
χ502-2-222-2002i−2i-22-22002i−2i−2i2i−2i2i0000002−2−22i2−i2−i2i2−2ζ2ζ00−2ζ32ζ300−1−i1+i1+i−1−i1−i−1+i−1+i1−i0000000000000000
χ512-2-222-2002i−2i-22-22002i−2i−2i2i−2i2i000000−222−2−i2i2i2−i22ζ−2ζ002ζ3−2ζ300−1−i1+i1+i−1−i1−i−1+i−1+i1−i0000000000000000
χ522-2-222-2002i−2i-22-22002i−2i−2i2i−2i2i000000−222−2−i2i2i2−i2−2ζ2ζ00−2ζ32ζ3001+i−1−i−1−i1+i−1+i1−i1−i−1+i0000000000000000
χ532-2-222-200−2i2i2-22-200−2i2i−2i2i−2i2i0000002−22−2−i2i2−i2i2002ζ−2ζ002ζ3−2ζ3−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ542-2-222-200−2i2i2-22-200−2i2i−2i2i−2i2i0000002−22−2−i2i2−i2i200−2ζ2ζ00−2ζ32ζ31+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ552-2-222-200−2i2i2-22-200−2i2i−2i2i−2i2i000000−22−22i2−i2i2−i2002ζ−2ζ002ζ3−2ζ31+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ562-2-222-200−2i2i2-22-200−2i2i−2i2i−2i2i000000−22−22i2−i2i2−i200−2ζ2ζ00−2ζ32ζ3−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ572-2-222-200−2i2i-22-2200−2i2i2i−2i2i−2i0000002−2−22−i2i2i2−i22ζ3−2ζ3002ζ−2ζ00−1+i1−i1−i−1+i1+i−1−i−1−i1+i0000000000000000
χ582-2-222-200−2i2i-22-2200−2i2i2i−2i2i−2i0000002−2−22−i2i2i2−i2−2ζ32ζ300−2ζ2ζ001−i−1+i−1+i1−i−1−i1+i1+i−1−i0000000000000000
χ592-2-222-200−2i2i-22-2200−2i2i2i−2i2i−2i000000−222−2i2−i2−i2i22ζ3−2ζ3002ζ−2ζ001−i−1+i−1+i1−i−1−i1+i1+i−1−i0000000000000000
χ602-2-222-200−2i2i-22-2200−2i2i2i−2i2i−2i000000−222−2i2−i2−i2i2−2ζ32ζ300−2ζ2ζ00−1+i1−i1−i−1+i1+i−1−i−1−i1+i0000000000000000
χ614-4-44-44004i−4i4-4-4400−4i4i4i−4i−4i4i0000000000000000000000000000000000000000000000
χ624-4-44-44004i−4i-444-400−4i4i−4i4i4i−4i0000000000000000000000000000000000000000000000
χ634-4-44-4400−4i4i4-4-44004i−4i−4i4i4i−4i0000000000000000000000000000000000000000000000
χ644-4-44-4400−4i4i-444-4004i−4i4i−4i−4i4i0000000000000000000000000000000000000000000000
χ6588-8-800000000008-80000000000000000000000000000000000000000000000000000
χ6688-8-80000000000-880000000000000000000000000000000000000000000000000000
χ678-88-8008-8000000000000000000000000000000000000000000000000000000000000
χ688-88-800-88000000000000000000000000000000000000000000000000000000000000

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