Finite Group Databasebeta

← Group #110850

Character table — Group #110850

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111111111111222222222222222244444444444444444444888888888888888888888888888888881616161616161616
order12222222444444442222444444444444444488888888888888884444444488888888888888888888888844448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-111-1-1111-1-1iiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-111-1-1ii−i−i
χ1011111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-111-1-1111-1-1iiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-1-1-1-111111111-1-1-1-1-1-111−i−iii
χ1111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-111-1-1111-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-1-1-1-11111-1-111−i−iii
χ1211111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-111-1-1111-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111-1-1-1-1111111-1-1ii−i−i
χ1311111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-111-1-1111-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111-1-1-1-1111111-1-1−i−iii
χ1411111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-111-1-1111-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111-1-111ii−i−i
χ1511111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-111-1-1111-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-111111111-1-1-1-1-1-111ii−i−i
χ1611111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-111-1-1111-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-111-1-1−i−iii
χ171-1-1-1-111111-1-1-1-11111-1-111-111-1-1-1-111-11-11-11111-1-1-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−i1-11-11-11-1
χ181-1-1-1-111111-1-1-1-11111-1-111-111-1-1-1-111-11-11-11111-1-1-1-11111-1-1-1-1ii−i−iii−i−i−i−iii−i−iii−i−iii−i−iiiii−i−iii−i−i-11-11-11-11
χ191-1-1-1-111111-1-1-1-11111-1-111-111-1-1-1-111-11-11-11111-1-1-1-11111-1-1-1-1−i−iii−i−iiiii−i−iii−i−iii−i−iii−i−i−i−iii−i−iii-11-11-11-11
χ201-1-1-1-111111-1-1-1-11111-1-111-111-1-1-1-111-11-11-11111-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii1-11-11-11-1
χ211-1-1-1-111111-1-1-1-11111-1-111-111-1-1-1-111-11-11-1-1-1-1-11111-1-1-1-11111ii−i−iii−i−iii−i−iii−i−i−i−iii−i−iii−i−iii−i−iii1-11-1-11-11
χ221-1-1-1-111111-1-1-1-11111-1-111-111-1-1-1-111-11-11-1-1-1-1-11111-1-1-1-11111ii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iii-11-111-11-1
χ231-1-1-1-111111-1-1-1-11111-1-111-111-1-1-1-111-11-11-1-1-1-1-11111-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i-11-111-11-1
χ241-1-1-1-111111-1-1-1-11111-1-111-111-1-1-1-111-11-11-1-1-1-1-11111-1-1-1-11111−i−iii−i−iii−i−iii−i−iiiii−i−iii−i−iii−i−iii−i−i1-11-1-11-11
χ251-1-1-1-1111-1-11111-1-1-1-11111-11111-1-1-1-1-11-1-11iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-11111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i1-1-11i−i−ii
χ261-1-1-1-1111-1-11111-1-1-1-11111-11111-1-1-1-1-11-1-11iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i-111-1−iii−i
χ271-1-1-1-1111-1-11111-1-1-1-11111-11111-1-1-1-1-11-1-11iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-111-1-1-1-111−i−iiiii−i−iii−i−i−i−iii-111-1−iii−i
χ281-1-1-1-1111-1-11111-1-1-1-11111-11111-1-1-1-1-11-1-11iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1-1-11111-1-1ii−i−i−i−iiiii−i−i−i−iii1-1-11i−i−ii
χ291-1-1-1-1111-1-11111-1-1-1-11111-11111-1-1-1-1-11-1-11−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-11111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii1-1-11−iii−i
χ301-1-1-1-1111-1-11111-1-1-1-11111-11111-1-1-1-1-11-1-11−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii-111-1i−i−ii
χ311-1-1-1-1111-1-11111-1-1-1-11111-11111-1-1-1-1-11-1-11−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-111-1-1-1-111ii−i−i−i−iii−i−iiiii−i−i-111-1i−i−ii
χ321-1-1-1-1111-1-11111-1-1-1-11111-11111-1-1-1-1-11-1-11−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1-1-11111-1-1−i−iiiii−i−i−i−iiiii−i−i1-1-11−iii−i
χ3322222222222222222222222-2-2-2-2-2-2-2-22-2-2-2-20000000000000000000000002-22-22-22-2000000000000000000000000
χ3422222222222222222222222-2-2-2-2-2-2-2-22-2-2-2-2000000000000000000000000-22-22-22-22000000000000000000000000
χ352222222222222222-2-2-2-2-2-2-222222222-2-2-2-2-222-2-222-2-222-2-222-2-20000000000000000000000000000000000000000
χ362222222222222222-2-2-2-2-2-2-222222222-2-2-2-2-2-2-222-2-222-2-222-2-2220000000000000000000000000000000000000000
χ372222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ382222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ3922222222-2-2-2-2-2-2-2-22222-2-2-222-2-222-2-2-2-2-2222i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-22222-2-2-222-2-222-2-2-2-2-222−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000000000
χ4122222222-2-2-2-2-2-2-2-22222-2-2-2-2-222-2-222-222-2-2000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ4222222222-2-2-2-2-2-2-2-22222-2-2-2-2-222-2-222-222-2-200000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ4322222222-2-2-2-2-2-2-2-2-2-2-2-2222-2-222-2-2222-2-2220000000000000000000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ4422222222-2-2-2-2-2-2-2-2-2-2-2-2222-2-222-2-2222-2-222000000000000000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ45222-2-2-22-22i−2i2i2i−2i−2i2i−2i00000002-22i−2i2-22i−2i00000002ζ3−2ζ3002ζ3−2ζ3002ζ−2ζ002ζ−2ζ1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000i2−i2i2−i22−22−200000000
χ46222-2-2-22-22i−2i2i2i−2i−2i2i−2i00000002-22i−2i2-22i−2i00000002ζ3−2ζ3002ζ3−2ζ3002ζ−2ζ002ζ−2ζ−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000−i2i2−i2i2−22−2200000000
χ47222-2-2-22-22i−2i2i2i−2i−2i2i−2i00000002-22i−2i2-22i−2i0000000−2ζ32ζ300−2ζ32ζ300−2ζ2ζ00−2ζ2ζ1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000−i2i2−i2i2−22−2200000000
χ48222-2-2-22-22i−2i2i2i−2i−2i2i−2i00000002-22i−2i2-22i−2i0000000−2ζ32ζ300−2ζ32ζ300−2ζ2ζ00−2ζ2ζ−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000i2−i2i2−i22−22−200000000
χ49222-2-2-22-2−2i2i−2i−2i2i2i−2i2i00000002-2−2i2i2-2−2i2i00000002ζ−2ζ002ζ−2ζ002ζ3−2ζ3002ζ3−2ζ31−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000i2−i2i2−i2−22−2200000000
χ50222-2-2-22-2−2i2i−2i−2i2i2i−2i2i00000002-2−2i2i2-2−2i2i00000002ζ−2ζ002ζ−2ζ002ζ3−2ζ3002ζ3−2ζ3−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000−i2i2−i2i22−22−200000000
χ51222-2-2-22-2−2i2i−2i−2i2i2i−2i2i00000002-2−2i2i2-2−2i2i0000000−2ζ2ζ00−2ζ2ζ00−2ζ32ζ300−2ζ32ζ31−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000−i2i2−i2i22−22−200000000
χ52222-2-2-22-2−2i2i−2i−2i2i2i−2i2i00000002-2−2i2i2-2−2i2i0000000−2ζ2ζ00−2ζ2ζ00−2ζ32ζ300−2ζ32ζ3−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000i2−i2i2−i2−22−2200000000
χ532-2-222-22-22i−2i−2i−2i2i2i2i−2i00000002-2−2i2i-222i−2i00000002ζ3−2ζ300−2ζ32ζ3002ζ−2ζ00−2ζ2ζ1−i−1+i−1+i1−i−1−i1+i1+i−1−i00000000000000002−2−22−i2i2i2−i200000000
χ542-2-222-22-22i−2i−2i−2i2i2i2i−2i00000002-2−2i2i-222i−2i00000002ζ3−2ζ300−2ζ32ζ3002ζ−2ζ00−2ζ2ζ−1+i1−i1−i−1+i1+i−1−i−1−i1+i0000000000000000−222−2i2−i2−i2i200000000
χ552-2-222-22-22i−2i−2i−2i2i2i2i−2i00000002-2−2i2i-222i−2i0000000−2ζ32ζ3002ζ3−2ζ300−2ζ2ζ002ζ−2ζ1−i−1+i−1+i1−i−1−i1+i1+i−1−i0000000000000000−222−2i2−i2−i2i200000000
χ562-2-222-22-22i−2i−2i−2i2i2i2i−2i00000002-2−2i2i-222i−2i0000000−2ζ32ζ3002ζ3−2ζ300−2ζ2ζ002ζ−2ζ−1+i1−i1−i−1+i1+i−1−i−1−i1+i00000000000000002−2−22−i2i2i2−i200000000
χ572-2-222-22-2−2i2i2i2i−2i−2i−2i2i00000002-22i−2i-22−2i2i00000002ζ−2ζ00−2ζ2ζ002ζ3−2ζ300−2ζ32ζ31+i−1−i−1−i1+i−1+i1−i1−i−1+i0000000000000000−222−2−i2i2i2−i200000000
χ582-2-222-22-2−2i2i2i2i−2i−2i−2i2i00000002-22i−2i-22−2i2i00000002ζ−2ζ00−2ζ2ζ002ζ3−2ζ300−2ζ32ζ3−1−i1+i1+i−1−i1−i−1+i−1+i1−i00000000000000002−2−22i2−i2−i2i200000000
χ592-2-222-22-2−2i2i2i2i−2i−2i−2i2i00000002-22i−2i-22−2i2i0000000−2ζ2ζ002ζ−2ζ00−2ζ32ζ3002ζ3−2ζ31+i−1−i−1−i1+i−1+i1−i1−i−1+i00000000000000002−2−22i2−i2−i2i200000000
χ602-2-222-22-2−2i2i2i2i−2i−2i−2i2i00000002-22i−2i-22−2i2i0000000−2ζ2ζ002ζ−2ζ00−2ζ32ζ3002ζ3−2ζ3−1−i1+i1+i−1−i1−i−1+i−1+i1−i0000000000000000−222−2−i2i2i2−i200000000
χ612-2-2-2-222222-2-2-2-22222-2-222-2-2-22222-2-2-2-22-220000000000000000000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ622-2-2-2-222222-2-2-2-22222-2-222-2-2-22222-2-2-2-22-22000000000000000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ632-2-2-2-222222-2-2-2-222-2-222-2-2222-2-2-2-2222-22-2222-2-2-2-22222-2-2-2-2220000000000000000000000000000000000000000
χ642-2-2-2-222222-2-2-2-222-2-222-2-2222-2-2-2-2222-22-22-2-22222-2-2-2-22222-2-20000000000000000000000000000000000000000
χ652-2-2-2-222222-2-2-2-222-2-222-2-22-2-22222-2-222-22-2000000000000000000000000000000002-2-222-2-220000000000000000
χ662-2-2-2-222222-2-2-2-222-2-222-2-22-2-22222-2-222-22-200000000000000000000000000000000-222-2-222-20000000000000000
χ672-2-2-2-2222-2-22222-2-222-2-2-2-222222-2-2-2-22-222-22i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000000000
χ682-2-2-2-2222-2-22222-2-222-2-2-2-222222-2-2-2-22-222-2−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000000000
χ692-2-2-2-2222-2-22222-2-222-2-2-2-22-2-2-2-2222222-2-22000000000000000000000000000000002-2-22-222-20000000000000000
χ702-2-2-2-2222-2-22222-2-222-2-2-2-22-2-2-2-2222222-2-2200000000000000000000000000000000-222-22-2-220000000000000000
χ712-2-2-2-2222-2-22222-2-2-2-22222-2-2-2-2-22222-2-222-20000000000000000000000002-2-22-222-2000000000000000000000000
χ722-2-2-2-2222-2-22222-2-2-2-22222-2-2-2-2-22222-2-222-2000000000000000000000000-222-22-2-22000000000000000000000000
χ73444-4-4-44-44i−4i4i4i−4i−4i4i−4i0000000-44−4i4i-44−4i4i0000000000000000000000000000000000000000000000000000000000000
χ74444-4-4-44-4−4i4i−4i−4i4i4i−4i4i0000000-444i−4i-444i−4i0000000000000000000000000000000000000000000000000000000000000
χ7544-44-44-4-4444-44-4-4-44-44-44-4-4000000004000000000000000000000000000000000000000000000000000000000000
χ7644-44-44-4-4444-44-4-4-4-44-44-44400000000-4000000000000000000000000000000000000000000000000000000000000
χ7744-44-44-4-4-4-4-44-44444-44-4-44400000000-4000000000000000000000000000000000000000000000000000000000000
χ7844-44-44-4-4-4-4-44-4444-44-444-4-4000000004000000000000000000000000000000000000000000000000000000000000
χ7944-4-44-4-444i−4i4i−4i−4i4i−4i4i000000000000000000002−2i−2+2i002−2i−2+2i002+2i−2−2i002+2i−2−2i000000000000000000000000000000000000000000
χ8044-4-44-4-444i−4i4i−4i−4i4i−4i4i00000000000000000000−2+2i2−2i00−2+2i2−2i00−2−2i2+2i00−2−2i2+2i000000000000000000000000000000000000000000
χ8144-4-44-4-44−4i4i−4i4i4i−4i4i−4i000000000000000000002+2i−2−2i002+2i−2−2i002−2i−2+2i002−2i−2+2i000000000000000000000000000000000000000000
χ8244-4-44-4-44−4i4i−4i4i4i−4i4i−4i00000000000000000000−2−2i2+2i00−2−2i2+2i00−2+2i2−2i00−2+2i2−2i000000000000000000000000000000000000000000
χ834-444-4-4-444i−4i−4i4i4i−4i−4i4i000000000000000000002−2i−2+2i00−2+2i2−2i002+2i−2−2i00−2−2i2+2i000000000000000000000000000000000000000000
χ844-444-4-4-444i−4i−4i4i4i−4i−4i4i00000000000000000000−2+2i2−2i002−2i−2+2i00−2−2i2+2i002+2i−2−2i000000000000000000000000000000000000000000
χ854-444-4-4-44−4i4i4i−4i−4i4i4i−4i000000000000000000002+2i−2−2i00−2−2i2+2i002−2i−2+2i00−2+2i2−2i000000000000000000000000000000000000000000
χ864-444-4-4-44−4i4i4i−4i−4i4i4i−4i00000000000000000000−2−2i2+2i002+2i−2−2i00−2+2i2−2i002−2i−2+2i000000000000000000000000000000000000000000
χ874-44-444-4-444-44-44-4-44-4-444-4400000000-4000000000000000000000000000000000000000000000000000000000000
χ884-44-444-4-444-44-44-4-4-444-4-44-4000000004000000000000000000000000000000000000000000000000000000000000
χ894-44-444-4-4-4-44-44-4444-4-44-44-4000000004000000000000000000000000000000000000000000000000000000000000
χ904-44-444-4-4-4-44-44-444-444-44-4400000000-4000000000000000000000000000000000000000000000000000000000000
χ914-4-444-44-44i−4i−4i−4i4i4i4i−4i0000000-444i−4i4-4−4i4i0000000000000000000000000000000000000000000000000000000000000
χ924-4-444-44-4−4i4i4i4i−4i−4i−4i4i0000000-44−4i4i4-44i−4i0000000000000000000000000000000000000000000000000000000000000

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