Finite Group Databasebeta

← Group #136643

Character table — Group #136643

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111122222222222222222244444488888888888888888888888816161616161616161616161616161616
order122222444444444444888888888824448888161616161616161616161616161616164444888888888888
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
χ51111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
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
χ9111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11-11-111-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i
χ10111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11-11-111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-1-111−i−iii−i−iii
χ11111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11-11-111-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii
χ12111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11-11-111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111ii−i−iii−i−i
χ13111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-11-11-1-111iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111ii−i−i−i−iii
χ14111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-11-11-1-111iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−i
χ15111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-11-11-1-111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111−i−iiiii−i−i
χ16111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-11-11-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1ii−i−i−i−iii
χ17222222222222222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ18222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ19222222-2-2-2-2-2-22222-2-22222-2-2-2-2222-22-2-2-22200000000000000000000000000000000
χ20222222-2-2-2-2-2-22222-2-22222-2-2-2-222-22-2222-2-200000000000000000000000000000000
χ212222-2-222-2-22222-2-2-2-2000000000022-2-20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ222222-2-222-2-22222-2-2-2-2000000000022-2-20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ232222-2-222-2-22222-2-2-2-20000000000-2-2220000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ242222-2-222-2-22222-2-2-2-20000000000-2-2220000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ252222-2-222-2-2-2-2-2-22222222222-2-2-2-2000000000000000000000000000000002-22-20000
χ262222-2-222-2-2-2-2-2-22222222222-2-2-2-200000000000000000000000000000000-22-220000
χ272222-2-222-2-2-2-2-2-22222-2-2-2-2-2-222220000000000000000000000000000000000002-22-2
χ282222-2-222-2-2-2-2-2-22222-2-2-2-2-2-22222000000000000000000000000000000000000-22-22
χ292222-2-2-2-22222-2-222-2-22222-2-222-2-20000000000000000000000000000000000002i−2i−2i2i
χ302222-2-2-2-22222-2-222-2-22222-2-222-2-2000000000000000000000000000000000000−2i2i2i−2i
χ312222-2-2-2-22222-2-222-2-2-2-2-2-222-2-222000000000000000000000000000000002i−2i−2i2i0000
χ322222-2-2-2-22222-2-222-2-2-2-2-2-222-2-22200000000000000000000000000000000−2i2i2i−2i0000
χ332222-2-2-2-222-2-222-2-22200000000002-2-22000022−2−2−2−22222−2−2−2−2220000000000000000
χ342222-2-2-2-222-2-222-2-22200000000002-2-220000−2−22222−2−2−2−22222−2−20000000000000000
χ352222-2-2-2-222-2-222-2-2220000000000-222-2000022−2−2−2−222−2−22222−2−20000000000000000
χ362222-2-2-2-222-2-222-2-2220000000000-222-20000−2−22222−2−222−2−2−2−2220000000000000000
χ372-22-22-22i−2i2i−2i2i−2i2-22-22i−2i000000000000002i−2i2-21+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ382-22-22-22i−2i2i−2i2i−2i2-22-22i−2i000000000000002i−2i2-2−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ392-22-22-22i−2i2i−2i2i−2i2-22-22i−2i00000000000000−2i2i-221+i−1−i1+i−1−i1−i−1+i1−i−1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ402-22-22-22i−2i2i−2i2i−2i2-22-22i−2i00000000000000−2i2i-22−1−i1+i−1−i1+i−1+i1−i−1+i1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ412-22-22-22i−2i2i−2i−2i2i-22-22−2i2i2i2i−2i−2i2-22-22i−2i00000000000000000000000000002-22i−2i00000000
χ422-22-22-22i−2i2i−2i−2i2i-22-22−2i2i2i2i−2i−2i2-22-22i−2i0000000000000000000000000000-22−2i2i00000000
χ432-22-22-22i−2i2i−2i−2i2i-22-22−2i2i−2i−2i2i2i-22-22−2i2i0000000000000000000000002-22i−2i000000000000
χ442-22-22-22i−2i2i−2i−2i2i-22-22−2i2i−2i−2i2i2i-22-22−2i2i000000000000000000000000-22−2i2i000000000000
χ452-22-22-2−2i2i−2i2i2i−2i-22-222i−2i2i2i−2i−2i-22-222i−2i0000000000000000000000002-2−2i2i000000000000
χ462-22-22-2−2i2i−2i2i2i−2i-22-222i−2i2i2i−2i−2i-22-222i−2i000000000000000000000000-222i−2i000000000000
χ472-22-22-2−2i2i−2i2i2i−2i-22-222i−2i−2i−2i2i2i2-22-2−2i2i00000000000000000000000000002-2−2i2i00000000
χ482-22-22-2−2i2i−2i2i2i−2i-22-222i−2i−2i−2i2i2i2-22-2−2i2i0000000000000000000000000000-222i−2i00000000
χ492-22-22-2−2i2i−2i2i−2i2i2-22-2−2i2i000000000000002i−2i-221−i−1+i1−i−1+i1+i−1−i1+i−1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ502-22-22-2−2i2i−2i2i−2i2i2-22-2−2i2i000000000000002i−2i-22−1+i1−i−1+i1−i−1−i1+i−1−i1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ512-22-22-2−2i2i−2i2i−2i2i2-22-2−2i2i00000000000000−2i2i2-21−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ522-22-22-2−2i2i−2i2i−2i2i2-22-2−2i2i00000000000000−2i2i2-2−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ532-22-2-222i−2i−2i2i2i−2i2-2-22−2i2i2i2i−2i−2i2-2-22−2i2i00000000000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ30000000000000000
χ542-22-2-222i−2i−2i2i2i−2i2-2-22−2i2i2i2i−2i−2i2-2-22−2i2i0000000000000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ30000000000000000
χ552-22-2-222i−2i−2i2i2i−2i2-2-22−2i2i−2i−2i2i2i-222-22i−2i000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ000000000000000000000000
χ562-22-2-222i−2i−2i2i2i−2i2-2-22−2i2i−2i−2i2i2i-222-22i−2i00000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ000000000000000000000000
χ572-22-2-22−2i2i2i−2i−2i2i2-2-222i−2i2i2i−2i−2i-222-2−2i2i000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ3000000000000000000000000
χ582-22-2-22−2i2i2i−2i−2i2i2-2-222i−2i2i2i−2i−2i-222-2−2i2i00000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ3000000000000000000000000
χ592-22-2-22−2i2i2i−2i−2i2i2-2-222i−2i−2i−2i2i2i2-2-222i−2i00000000000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ0000000000000000
χ602-22-2-22−2i2i2i−2i−2i2i2-2-222i−2i−2i−2i2i2i2-2-222i−2i0000000000000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ0000000000000000
χ614444444444-4-4-4-4-4-4-4-400000000000000000000000000000000000000000000000000
χ62444444-4-4-4-444-4-4-4-44400000000000000000000000000000000000000000000000000
χ634-44-4-444i−4i−4i4i−4i4i-444-44i−4i00000000000000000000000000000000000000000000000000
χ644-44-4-44−4i4i4i−4i4i−4i-444-4−4i4i00000000000000000000000000000000000000000000000000
χ6588-8-80000000000000042−4242−420000000000000000000000000000000000000000000000
χ6688-8-800000000000000−4242−42420000000000000000000000000000000000000000000000
χ678-8-88000000000000004i2−4i2−4i24i20000000000000000000000000000000000000000000000
χ688-8-8800000000000000−4i24i24i2−4i20000000000000000000000000000000000000000000000

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