Finite Group Databasebeta

← Group #208982

Character table — Group #208982

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111111112222222222222222444444444444448888888888888888888888888888888888888888888816161616
order12222222222244444444444422224444444444222244444444444444444444444488888888888888882244
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ5111111111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111-1-111-1-111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ7111111111111111111111111-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-111-1-111-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ8111111111111111111111111-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ9111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ10111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111
χ11111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ12111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-11111-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-11111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1
χ171-1111-1-1-11-11-1ii−i−iiiii−i−i−i−i11-1-1i−iii−i−i11-1-11-11-11-1i−i1-11-1i−ii−ii−ii−i11-1-1ii−i−i11-1-1ii−i−i11-1-1ii−i−i1-1i−i
χ181-1111-1-1-11-11-1ii−i−iiiii−i−i−i−i11-1-1i−iii−i−i11-1-11-11-11-1i−i1-11-1i−ii−ii−ii−i-1-111−i−iii-1-111−i−iii-1-111−i−iii-11−ii
χ191-1111-1-1-11-11-1ii−i−iiiii−i−i−i−i11-1-1i−iii−i−i11-1-1-11-111-1i−i-11-11−ii−ii−ii−ii11-1-1ii−i−i-1-111−i−iii-1-111−i−iii1-1i−i
χ201-1111-1-1-11-11-1ii−i−iiiii−i−i−i−i11-1-1i−iii−i−i11-1-1-11-111-1i−i-11-11−ii−ii−ii−ii-1-111−i−iii11-1-1ii−i−i11-1-1ii−i−i-11−ii
χ211-1111-1-1-11-11-1ii−i−iiiii−i−i−i−i-1-111i−i−i−iii11-1-11-1-11-11−ii1-1-11i−i−iii−i−ii11-1-1ii−i−i11-1-1ii−i−i-1-111−i−iii-11−ii
χ221-1111-1-1-11-11-1ii−i−iiiii−i−i−i−i-1-111i−i−i−iii11-1-11-1-11-11−ii1-1-11i−i−iii−i−ii-1-111−i−iii-1-111−i−iii11-1-1ii−i−i1-1i−i
χ231-1111-1-1-11-11-1ii−i−iiiii−i−i−i−i-1-111i−i−i−iii11-1-1-111-1-11−ii-111-1−iii−i−iii−i11-1-1ii−i−i-1-111−i−iii11-1-1ii−i−i-11−ii
χ241-1111-1-1-11-11-1ii−i−iiiii−i−i−i−i-1-111i−i−i−iii11-1-1-111-1-11−ii-111-1−iii−i−iii−i-1-111−i−iii11-1-1ii−i−i-1-111−i−iii1-1i−i
χ251-1111-1-1-11-11-1−i−iii−i−i−i−iiiii11-1-1−ii−i−iii11-1-11-11-11-1−ii1-11-1−ii−ii−ii−ii11-1-1−i−iii11-1-1−i−iii11-1-1−i−iii1-1−ii
χ261-1111-1-1-11-11-1−i−iii−i−i−i−iiiii11-1-1−ii−i−iii11-1-11-11-11-1−ii1-11-1−ii−ii−ii−ii-1-111ii−i−i-1-111ii−i−i-1-111ii−i−i-11i−i
χ271-1111-1-1-11-11-1−i−iii−i−i−i−iiiii11-1-1−ii−i−iii11-1-1-11-111-1−ii-11-11i−ii−ii−ii−i11-1-1−i−iii-1-111ii−i−i-1-111ii−i−i1-1−ii
χ281-1111-1-1-11-11-1−i−iii−i−i−i−iiiii11-1-1−ii−i−iii11-1-1-11-111-1−ii-11-11i−ii−ii−ii−i-1-111ii−i−i11-1-1−i−iii11-1-1−i−iii-11i−i
χ291-1111-1-1-11-11-1−i−iii−i−i−i−iiiii-1-111−iiii−i−i11-1-11-1-11-11i−i1-1-11−iii−i−iii−i11-1-1−i−iii11-1-1−i−iii-1-111ii−i−i-11i−i
χ301-1111-1-1-11-11-1−i−iii−i−i−i−iiiii-1-111−iiii−i−i11-1-11-1-11-11i−i1-1-11−iii−i−iii−i-1-111ii−i−i-1-111ii−i−i11-1-1−i−iii1-1−ii
χ311-1111-1-1-11-11-1−i−iii−i−i−i−iiiii-1-111−iiii−i−i11-1-1-111-1-11i−i-111-1i−i−iii−i−ii11-1-1−i−iii-1-111ii−i−i11-1-1−i−iii-11i−i
χ321-1111-1-1-11-11-1−i−iii−i−i−i−iiiii-1-111−iiii−i−i11-1-1-111-1-11i−i-111-1i−i−iii−i−ii-1-111ii−i−i11-1-1−i−iii-1-111ii−i−i1-1−ii
χ332222222222222222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-20000-2-2220000000000000000000000000000000000000000
χ342222222222222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2-2-2000022-2-20000000000000000000000000000000000000000
χ35222222222222-2-2-2-2222222222222-2-22222-2-2-2-20000-2-2-2-20000000000000000000000000000000000000000
χ36222222222222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2000022220000000000000000000000000000000000000000
χ3722222222-2-2-2-2222222-2-222-2-20000-2-200002-22-20022000000-2-200-2-200220000000000000000000000000000
χ3822222222-2-2-2-2222222-2-222-2-20000-2-200002-22-200-2-200000022002200-2-20000000000000000000000000000
χ3922222222-2-2-2-22222-2-222-2-2220000-2-20000-22-2222000000-2-200-2-20022000000000000000000000000000000
χ4022222222-2-2-2-22222-2-222-2-2220000-2-20000-22-22-2-200000022002200-2-2000000000000000000000000000000
χ4122222222-2-2-2-2-2-2-2-222-2-222-2-20000220000-22-2222000000-2-2002200-2-2000000000000000000000000000000
χ4222222222-2-2-2-2-2-2-2-222-2-222-2-20000220000-22-22-2-20000002200-2-20022000000000000000000000000000000
χ4322222222-2-2-2-2-2-2-2-2-2-222-2-22200002200002-22-20022000000-2-2002200-2-20000000000000000000000000000
χ4422222222-2-2-2-2-2-2-2-2-2-222-2-22200002200002-22-200-2-20000002200-2-200220000000000000000000000000000
χ4522-2-222-2-2-222-200002i−2i2i−2i2i−2i2i−2i2-22-2002i−2i2i−2i000000000000000000000000000000002−22−2i2−i2i2−i22−22−2i2−i2i2−i20000
χ4622-2-222-2-2-222-200002i−2i2i−2i2i−2i2i−2i2-22-2002i−2i2i−2i00000000000000000000000000000000−22−22−i2i2−i2i2−22−22−i2i2−i2i20000
χ4722-2-222-2-2-222-200002i−2i2i−2i2i−2i2i−2i-22-2200−2i2i−2i2i000000000000000000000000000000002−22−2i2−i2i2−i2−22−22−i2i2−i2i20000
χ4822-2-222-2-2-222-200002i−2i2i−2i2i−2i2i−2i-22-2200−2i2i−2i2i00000000000000000000000000000000−22−22−i2i2−i2i22−22−2i2−i2i2−i20000
χ4922-2-222-2-2-222-20000−2i2i−2i2i−2i2i−2i2i2-22-200−2i2i−2i2i000000000000000000000000000000002−22−2−i2i2−i2i22−22−2−i2i2−i2i20000
χ5022-2-222-2-2-222-20000−2i2i−2i2i−2i2i−2i2i2-22-200−2i2i−2i2i00000000000000000000000000000000−22−22i2−i2i2−i2−22−22i2−i2i2−i20000
χ5122-2-222-2-2-222-20000−2i2i−2i2i−2i2i−2i2i-22-22002i−2i2i−2i000000000000000000000000000000002−22−2−i2i2−i2i2−22−22i2−i2i2−i20000
χ5222-2-222-2-2-222-20000−2i2i−2i2i−2i2i−2i2i-22-22002i−2i2i−2i00000000000000000000000000000000−22−22i2−i2i2−i22−22−2−i2i2−i2i20000
χ532-2222-2-2-22-22-22i2i−2i−2i−2i−2i−2i−2i2i2i2i2i22-2-22i−2i−2i−2i2i2i-2-2220000-222i−2i0000000000000000000000000000000000000000
χ542-2222-2-2-22-22-22i2i−2i−2i−2i−2i−2i−2i2i2i2i2i-2-2222i−2i2i2i−2i−2i-2-22200002-2−2i2i0000000000000000000000000000000000000000
χ552-2222-2-2-22-22-2−2i−2i2i2i2i2i2i2i−2i−2i−2i−2i22-2-2−2i2i2i2i−2i−2i-2-2220000-22−2i2i0000000000000000000000000000000000000000
χ562-2222-2-2-22-22-2−2i−2i2i2i2i2i2i2i−2i−2i−2i−2i-2-222−2i2i−2i−2i2i2i-2-22200002-22i−2i0000000000000000000000000000000000000000
χ572-2222-2-2-2-22-222i2i−2i−2i2i2i−2i−2i−2i−2i2i2i0000−2i2i00002-2-22002-2000000-2200−2i2i002i−2i0000000000000000000000000000
χ582-2222-2-2-2-22-222i2i−2i−2i2i2i−2i−2i−2i−2i2i2i0000−2i2i00002-2-2200-220000002-2002i−2i00−2i2i0000000000000000000000000000
χ592-2222-2-2-2-22-222i2i−2i−2i−2i−2i2i2i2i2i−2i−2i0000−2i2i0000-222-22-2000000-2200−2i2i002i−2i000000000000000000000000000000
χ602-2222-2-2-2-22-222i2i−2i−2i−2i−2i2i2i2i2i−2i−2i0000−2i2i0000-222-2-220000002-2002i−2i00−2i2i000000000000000000000000000000
χ612-2222-2-2-2-22-22−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i00002i−2i0000-222-22-2000000-22002i−2i00−2i2i000000000000000000000000000000
χ622-2222-2-2-2-22-22−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i00002i−2i0000-222-2-220000002-200−2i2i002i−2i000000000000000000000000000000
χ632-2222-2-2-2-22-22−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i00002i−2i00002-2-22002-2000000-22002i−2i00−2i2i0000000000000000000000000000
χ642-2222-2-2-2-22-22−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i00002i−2i00002-2-2200-220000002-200−2i2i002i−2i0000000000000000000000000000
χ652-2-2-22-222-2-22200002-22-2-22-222-2-22002-2-22000000000000000000000000000000002−2−222−2−222−2−222−2−220000
χ662-2-2-22-222-2-22200002-22-2-22-222-2-22002-2-2200000000000000000000000000000000−222−2−222−2−222−2−222−20000
χ672-2-2-22-222-2-22200002-22-2-22-22-222-200-222-2000000000000000000000000000000002−2−222−2−22−222−2−222−20000
χ682-2-2-22-222-2-22200002-22-2-22-22-222-200-222-200000000000000000000000000000000−222−2−222−22−2−222−2−220000
χ692-2-2-22-222-2-2220000-22-222-22-22-2-2200-222-2000000000000000000000000000000002−2−22−222−22−2−22−222−20000
χ702-2-2-22-222-2-2220000-22-222-22-22-2-2200-222-200000000000000000000000000000000−222−22−2−22−222−22−2−220000
χ712-2-2-22-222-2-2220000-22-222-22-2-222-2002-2-22000000000000000000000000000000002−2−22−222−2−222−22−2−220000
χ722-2-2-22-222-2-2220000-22-222-22-2-222-2002-2-2200000000000000000000000000000000−222−22−2−222−2−22−222−20000
χ73444-4-4-44-400004i−4i4i−4i0000000000000000000000000000000000000000002-22-22i−2i2i−2i00000000000000000000
χ74444-4-4-44-400004i−4i4i−4i000000000000000000000000000000000000000000-22-22−2i2i−2i2i00000000000000000000
χ75444-4-4-44-40000−4i4i−4i4i0000000000000000000000000000000000000000002-22-2−2i2i−2i2i00000000000000000000
χ76444-4-4-44-40000−4i4i−4i4i000000000000000000000000000000000000000000-22-222i−2i2i−2i00000000000000000000
χ7744-4-444-4-44-4-4400004i−4i−4i4i4i−4i−4i4i00000000000000000000000000000000000000000000000000000000000000
χ7844-4-444-4-44-4-440000−4i4i4i−4i−4i4i4i−4i00000000000000000000000000000000000000000000000000000000000000
χ794-44-4-44-4400004-4-440000000000000000000000000000000000000000002-2-222-2-2200000000000000000000
χ804-44-4-44-4400004-4-44000000000000000000000000000000000000000000-222-2-222-200000000000000000000
χ814-44-4-44-440000-444-40000000000000000000000000000000000000000002-2-22-222-200000000000000000000
χ824-44-4-44-440000-444-4000000000000000000000000000000000000000000-222-22-2-2200000000000000000000
χ834-4-4-44-44444-4-400004-4-44-444-400000000000000000000000000000000000000000000000000000000000000
χ844-4-4-44-44444-4-40000-444-44-4-4400000000000000000000000000000000000000000000000000000000000000
χ8588-88-8-8-88000000000000000000000000000000000000000000000000000000000000000000000000000000
χ868-8-88-888-8000000000000000000000000000000000000000000000000000000000000000000000000000000

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