Finite Group Databasebeta

← Group #211523

Character table — Group #211523

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1111111122222222222222224444444444444444444444888888888888888888888888888888881616161616161616
order12222222444444444444444444444488888888888888884444444488888888888888888888888844444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-11111111111-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ1011111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-111-1-111
χ1111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-111-1-111
χ1211111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111-1-111111111111111-1-111-1-1
χ1311111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111111111-1-111-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ1411111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111111111-1-111-1-111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1-1-11111-1-1
χ1511111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1111111-1-1-1-11111-1-11111-1-1
χ1611111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-11111111111-1-1-1-111-1-1-1-111
χ171-11-11-11-1ii−i−iii−i−i11-1-1-11-111-1i−ii−i11-1-1ii−i−iiiii−i−i−i−ii−i1-1i−i1-1ii−i−iii−i−i1-1i−i11-1-111-1-111-1-11-1i−i1-1i−i
χ181-11-11-11-1ii−i−iii−i−i11-1-1-11-111-1i−ii−i11-1-1ii−i−iiiii−i−i−i−ii−i1-1i−i1-1−i−iii−i−iii1-1i−i11-1-1-1-111-1-111-11−ii-11−ii
χ191-11-11-11-1ii−i−iii−i−i11-1-1-11-111-1i−ii−i11-1-1ii−i−i−i−i−i−iiiii−ii-11−ii-11ii−i−iii−i−i1-1i−i-1-11111-1-111-1-1-11−ii-11−ii
χ201-11-11-11-1ii−i−iii−i−i11-1-1-11-111-1i−ii−i11-1-1ii−i−i−i−i−i−iiiii−ii-11−ii-11−i−iii−i−iii1-1i−i-1-111-1-111-1-1111-1i−i1-1i−i
χ211-11-11-11-1ii−i−iii−i−i11-1-1-11-111-1i−ii−i-1-111−i−iiiiiii−i−i−i−i−ii-11−ii-11ii−i−i−i−iii-11−ii11-1-111-1-1-1-1111-1i−i-11−ii
χ221-11-11-11-1ii−i−iii−i−i11-1-1-11-111-1i−ii−i-1-111−i−iiiiiii−i−i−i−i−ii-11−ii-11−i−iiiii−i−i-11−ii11-1-1-1-11111-1-1-11−ii1-1i−i
χ231-11-11-11-1ii−i−iii−i−i11-1-1-11-111-1i−ii−i-1-111−i−iii−i−i−i−iiiiii−i1-1i−i1-1ii−i−i−i−iii-11−ii-1-11111-1-1-1-111-11−ii1-1i−i
χ241-11-11-11-1ii−i−iii−i−i11-1-1-11-111-1i−ii−i-1-111−i−iii−i−i−i−iiiiii−i1-1i−i1-1−i−iiiii−i−i-11−ii-1-111-1-11111-1-11-1i−i-11−ii
χ251-11-11-11-1−i−iii−i−iii11-1-1-11-111-1−ii−ii11-1-1−i−iiiiiii−i−i−i−ii−i-11i−i-11ii−i−iii−i−i1-1−ii-1-111-1-111-1-1111-1−ii1-1−ii
χ261-11-11-11-1−i−iii−i−iii11-1-1-11-111-1−ii−ii11-1-1−i−iiiiiii−i−i−i−ii−i-11i−i-11−i−iii−i−iii1-1−ii-1-11111-1-111-1-1-11i−i-11i−i
χ271-11-11-11-1−i−iii−i−iii11-1-1-11-111-1−ii−ii11-1-1−i−iii−i−i−i−iiiii−ii1-1−ii1-1ii−i−iii−i−i1-1−ii11-1-1-1-111-1-111-11i−i-11i−i
χ281-11-11-11-1−i−iii−i−iii11-1-1-11-111-1−ii−ii11-1-1−i−iii−i−i−i−iiiii−ii1-1−ii1-1−i−iii−i−iii1-1−ii11-1-111-1-111-1-11-1−ii1-1−ii
χ291-11-11-11-1−i−iii−i−iii11-1-1-11-111-1−ii−ii-1-111ii−i−iiiii−i−i−i−i−ii1-1−ii1-1ii−i−i−i−iii-11i−i-1-111-1-11111-1-11-1−ii-11i−i
χ301-11-11-11-1−i−iii−i−iii11-1-1-11-111-1−ii−ii-1-111ii−i−iiiii−i−i−i−i−ii1-1−ii1-1−i−iiiii−i−i-11i−i-1-11111-1-1-1-111-11i−i1-1−ii
χ311-11-11-11-1−i−iii−i−iii11-1-1-11-111-1−ii−ii-1-111ii−i−i−i−i−i−iiiiii−i-11i−i-11ii−i−i−i−iii-11i−i11-1-1-1-11111-1-1-11i−i1-1−ii
χ321-11-11-11-1−i−iii−i−iii11-1-1-11-111-1−ii−ii-1-111ii−i−i−i−i−i−iiiiii−i-11i−i-11−i−iiiii−i−i-11i−i11-1-111-1-1-1-1111-1−ii-11i−i
χ332222222222222222-222-2-222-2-2-2-2-2-2-222222222000000000000000000000000-2-2-2-200000000000000000000
χ342222222222222222-222-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000222200000000000000000000
χ35222222222222-2-2-2-22-2-222-2-22-2-222-2-200000000000000002222-2-2-2-200000000000000000000000000000000
χ36222222222222-2-2-2-22-2-222-2-22-2-222-2-20000000000000000-2-2-2-2222200000000000000000000000000000000
χ37222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-222000000002i2i−2i−2i2i2i−2i−2i000000000000000000002i−2i2i−2i0000000000000000
χ38222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-22200000000−2i−2i2i2i−2i−2i2i2i00000000000000000000−2i2i−2i2i0000000000000000
χ3922222222-2-2-2-222222-2-222-2-22-2-2-2-222000000000000000022-2-2-2-22200000000000000000000000000000000
χ4022222222-2-2-2-222222-2-222-2-22-2-2-2-2220000000000000000-2-22222-2-200000000000000000000000000000000
χ4122222222-2-2-2-22222-2-2-2-2-2-2-2-22222-2-2000000002i2i−2i−2i2i2i−2i−2i00000000000000000000−2i2i−2i2i0000000000000000
χ4222222222-2-2-2-22222-2-2-2-2-2-2-2-22222-2-200000000−2i−2i2i2i−2i−2i2i2i000000000000000000002i−2i2i−2i0000000000000000
χ4322222222-2-2-2-2-2-2-2-2-222-2-222-2-2-222222222-2-2-2-2000000000000000000000000-2-22200000000000000000000
χ4422222222-2-2-2-2-2-2-2-2-222-2-222-2-2-22222-2-2-2-2222200000000000000000000000022-2-200000000000000000000
χ4522-2-222-2-22-22-22-22-20-2-2002200000002i−2i2i−2i2i−2i2i−2i00000000000000002−22−2i2−i2i2−i2000000002−22−2i2−i2i2−i200000000
χ4622-2-222-2-22-22-22-22-20-2-2002200000002i−2i2i−2i2i−2i2i−2i0000000000000000−22−22−i2i2−i2i200000000−22−22−i2i2−i2i200000000
χ4722-2-222-2-22-22-22-22-20-2-200220000000−2i2i−2i2i−2i2i−2i2i00000000000000002−22−2−i2i2−i2i2000000002−22−2−i2i2−i2i200000000
χ4822-2-222-2-22-22-22-22-20-2-200220000000−2i2i−2i2i−2i2i−2i2i0000000000000000−22−22i2−i2i2−i200000000−22−22i2−i2i2−i200000000
χ4922-2-222-2-2-22-22-22-220-2-2002200000002i−2i2i−2i−2i2i−2i2i00000000000000002−22−2i2−i2i2−i200000000−22−22−i2i2−i2i200000000
χ5022-2-222-2-2-22-22-22-220-2-2002200000002i−2i2i−2i−2i2i−2i2i0000000000000000−22−22−i2i2−i2i2000000002−22−2i2−i2i2−i200000000
χ5122-2-222-2-2-22-22-22-220-2-200220000000−2i2i−2i2i2i−2i2i−2i00000000000000002−22−2−i2i2−i2i200000000−22−22i2−i2i2−i200000000
χ5222-2-222-2-2-22-22-22-220-2-200220000000−2i2i−2i2i2i−2i2i−2i0000000000000000−22−22i2−i2i2−i2000000002−22−2−i2i2−i2i200000000
χ532-22-22-22-22i2i−2i−2i2i2i−2i−2i-22-2222-2-2-22−2i2i−2i2i22-2-22i2i−2i−2i000000000000000000000000-22−2i2i00000000000000000000
χ542-22-22-22-22i2i−2i−2i2i2i−2i−2i-22-2222-2-2-22−2i2i−2i2i-2-222−2i−2i2i2i0000000000000000000000002-22i−2i00000000000000000000
χ552-22-22-22-22i2i−2i−2i−2i−2i2i2i2-22-2-2-222-222i−2i−2i2i00000000000000002i−2i2-2−2i2i-2200000000000000000000000000000000
χ562-22-22-22-22i2i−2i−2i−2i−2i2i2i2-22-2-2-222-222i−2i−2i2i0000000000000000−2i2i-222i−2i2-200000000000000000000000000000000
χ572-22-22-22-22i2i−2i−2i−2i−2i2i2i-2-2222-22-22-2−2i2i2i−2i0000000022-2-2-2-22200000000000000000000−2i2i2i−2i0000000000000000
χ582-22-22-22-22i2i−2i−2i−2i−2i2i2i-2-2222-22-22-2−2i2i2i−2i00000000-2-22222-2-2000000000000000000002i−2i−2i2i0000000000000000
χ592-22-22-22-2−2i−2i2i2i2i2i−2i−2i2-22-2-2-222-22−2i2i2i−2i00000000000000002i−2i-22−2i2i2-200000000000000000000000000000000
χ602-22-22-22-2−2i−2i2i2i2i2i−2i−2i2-22-2-2-222-22−2i2i2i−2i0000000000000000−2i2i2-22i−2i-2200000000000000000000000000000000
χ612-22-22-22-2−2i−2i2i2i2i2i−2i−2i-2-2222-22-22-22i−2i−2i2i0000000022-2-2-2-222000000000000000000002i−2i−2i2i0000000000000000
χ622-22-22-22-2−2i−2i2i2i2i2i−2i−2i-2-2222-22-22-22i−2i−2i2i00000000-2-22222-2-200000000000000000000−2i2i2i−2i0000000000000000
χ632-22-22-22-2−2i−2i2i2i−2i−2i2i2i-22-2222-2-2-222i−2i2i−2i22-2-2−2i−2i2i2i000000000000000000000000-222i−2i00000000000000000000
χ642-22-22-22-2−2i−2i2i2i−2i−2i2i2i-22-2222-2-2-222i−2i2i−2i-2-2222i2i−2i−2i0000000000000000000000002-2−2i2i00000000000000000000
χ652-2-222-2-222i−2i−2i2i2i−2i−2i2i0-22002-200000002i−2i−2i2i-222-20000000000000000i2−i2−i2i2−222−2000000002−2−22i2−i2−i2i200000000
χ662-2-222-2-222i−2i−2i2i2i−2i−2i2i0-22002-200000002i−2i−2i2i-222-20000000000000000−i2i2i2−i22−2−2200000000−222−2−i2i2i2−i200000000
χ672-2-222-2-222i−2i−2i2i2i−2i−2i2i0-22002-20000000−2i2i2i−2i2-2-220000000000000000i2−i2−i2i22−2−22000000002−2−22−i2i2i2−i200000000
χ682-2-222-2-222i−2i−2i2i2i−2i−2i2i0-22002-20000000−2i2i2i−2i2-2-220000000000000000−i2i2i2−i2−222−200000000−222−2i2−i2−i2i200000000
χ692-2-222-2-22−2i2i2i−2i−2i2i2i−2i0-22002-200000002i−2i−2i2i2-2-220000000000000000i2−i2−i2i2−222−200000000−222−2−i2i2i2−i200000000
χ702-2-222-2-22−2i2i2i−2i−2i2i2i−2i0-22002-200000002i−2i−2i2i2-2-220000000000000000−i2i2i2−i22−2−22000000002−2−22i2−i2−i2i200000000
χ712-2-222-2-22−2i2i2i−2i−2i2i2i−2i0-22002-20000000−2i2i2i−2i-222-20000000000000000i2−i2−i2i22−2−2200000000−222−2i2−i2−i2i200000000
χ722-2-222-2-22−2i2i2i−2i−2i2i2i−2i0-22002-20000000−2i2i2i−2i-222-20000000000000000−i2i2i2−i2−222−2000000002−2−22−i2i2i2−i200000000
χ7344-44-4-44-4000000004004-400-40000000000000022−2222−2222−2222−220000000000000000000000000000000000000000
χ7444-44-4-44-4000000004004-400-400000000000000−2222−2222−2222−22220000000000000000000000000000000000000000
χ7544-44-4-44-400000000-400-44004000000000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000000000000000
χ7644-44-4-44-400000000-400-4400400000000000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000000000000000
χ7744-4-444-4-44-44-4-44-4404400-4-4000000000000000000000000000000000000000000000000000000000000000
χ7844-4-444-4-4-44-444-44-404400-4-4000000000000000000000000000000000000000000000000000000000000000
χ794-4-444-4-444i−4i−4i4i−4i4i4i−4i04-400-44000000000000000000000000000000000000000000000000000000000000000
χ804-4-444-4-44−4i4i4i−4i4i−4i−4i4i04-400-44000000000000000000000000000000000000000000000000000000000000000
χ814-4-4-4-444400000000400-4400-4000000000000002i2−2i22i2−2i2−2i22i2−2i22i20000000000000000000000000000000000000000
χ824-4-4-4-444400000000400-4400-400000000000000−2i22i2−2i22i22i2−2i22i2−2i20000000000000000000000000000000000000000
χ834-4-4-4-444400000000-4004-40040000000000000022−22−2222−222222−220000000000000000000000000000000000000000
χ844-4-4-4-444400000000-4004-400400000000000000−222222−2222−22−22220000000000000000000000000000000000000000
χ85888-8-8-8-88000000000000000000000000000000000000000000000000000000000000000000000000000000
χ868-888-88-8-8000000000000000000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).