Finite Group Databasebeta

← Group #210074

Character table — Group #210074

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1111111122222222222222224444444444444444444444888888888888888888888888888888881616161616161616
order12222222444444444444444444444444444444444444442222224444444444888888888888888844448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ911111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1
χ1011111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111
χ1111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-111
χ1211111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1111111-1-111-1-1
χ1311111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ1411111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-111-1-1111111-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ1511111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ1611111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-11111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111
χ171-11-111-1-1ii−i−i11-1-1ii−i−i11-1-1i−ii−i11-1-1ii−i−i11-1-1ii−i−i1-11-111-1-11-1i−ii−iii−i−i11-1-1ii−i−i11-1-1ii−i−i1-1i−i1-1i−i
χ181-11-111-1-1ii−i−i11-1-1ii−i−i11-1-1i−ii−i11-1-1ii−i−i11-1-1ii−i−i1-11-111-1-11-1i−ii−iii−i−i-1-111−i−iii-1-111−i−iii-11−ii-11−ii
χ191-11-111-1-1ii−i−i11-1-1ii−i−i11-1-1i−ii−i11-1-1ii−i−i-1-111−i−iii1-11-1-1-111-11−iii−i−i−iii11-1-1ii−i−i11-1-1ii−i−i-11−ii-11−ii
χ201-11-111-1-1ii−i−i11-1-1ii−i−i11-1-1i−ii−i11-1-1ii−i−i-1-111−i−iii1-11-1-1-111-11−iii−i−i−iii-1-111−i−iii-1-111−i−iii1-1i−i1-1i−i
χ211-11-111-1-1ii−i−i11-1-1ii−i−i11-1-1i−ii−i-1-111−i−iii11-1-1ii−i−i1-1-11-1-1111-1i−i−ii−i−iii11-1-1ii−i−i-1-111−i−iii1-1i−i-11−ii
χ221-11-111-1-1ii−i−i11-1-1ii−i−i11-1-1i−ii−i-1-111−i−iii11-1-1ii−i−i1-1-11-1-1111-1i−i−ii−i−iii-1-111−i−iii11-1-1ii−i−i-11−ii1-1i−i
χ231-11-111-1-1ii−i−i11-1-1ii−i−i11-1-1i−ii−i-1-111−i−iii-1-111−i−iii1-1-1111-1-1-11−ii−iiii−i−i11-1-1ii−i−i-1-111−i−iii-11−ii1-1i−i
χ241-11-111-1-1ii−i−i11-1-1ii−i−i11-1-1i−ii−i-1-111−i−iii-1-111−i−iii1-1-1111-1-1-11−ii−iiii−i−i-1-111−i−iii11-1-1ii−i−i1-1i−i-11−ii
χ251-11-111-1-1−i−iii11-1-1−i−iii11-1-1−ii−ii11-1-1−i−iii11-1-1−i−iii1-11-111-1-11-1−ii−ii−i−iii11-1-1−i−iii11-1-1−i−iii1-1−ii1-1−ii
χ261-11-111-1-1−i−iii11-1-1−i−iii11-1-1−ii−ii11-1-1−i−iii11-1-1−i−iii1-11-111-1-11-1−ii−ii−i−iii-1-111ii−i−i-1-111ii−i−i-11i−i-11i−i
χ271-11-111-1-1−i−iii11-1-1−i−iii11-1-1−ii−ii11-1-1−i−iii-1-111ii−i−i1-11-1-1-111-11i−i−iiii−i−i11-1-1−i−iii11-1-1−i−iii-11i−i-11i−i
χ281-11-111-1-1−i−iii11-1-1−i−iii11-1-1−ii−ii11-1-1−i−iii-1-111ii−i−i1-11-1-1-111-11i−i−iiii−i−i-1-111ii−i−i-1-111ii−i−i1-1−ii1-1−ii
χ291-11-111-1-1−i−iii11-1-1−i−iii11-1-1−ii−ii-1-111ii−i−i11-1-1−i−iii1-1-11-1-1111-1−iii−iii−i−i11-1-1−i−iii-1-111ii−i−i1-1−ii-11i−i
χ301-11-111-1-1−i−iii11-1-1−i−iii11-1-1−ii−ii-1-111ii−i−i11-1-1−i−iii1-1-11-1-1111-1−iii−iii−i−i-1-111ii−i−i11-1-1−i−iii-11i−i1-1−ii
χ311-11-111-1-1−i−iii11-1-1−i−iii11-1-1−ii−ii-1-111ii−i−i-1-111ii−i−i1-1-1111-1-1-11i−ii−i−i−iii11-1-1−i−iii-1-111ii−i−i-11i−i1-1−ii
χ321-11-111-1-1−i−iii11-1-1−i−iii11-1-1−ii−ii-1-111ii−i−i-1-111ii−i−i1-1-1111-1-1-11i−ii−i−i−iii-1-111ii−i−i11-1-1−i−iii1-1−ii-11i−i
χ332222222222222-22-222222-22-2-2-2-2-22222222200000000-2-2-2-200000000-2-20000000000000000000000000000
χ342222222222222-22-222222-22-2-2-2-2-2-2-2-2-2-2-2-2-200000000-2-22200000000220000000000000000000000000000
χ35222222222222-22-22-2-2-2-2-22-2222-2-2000000002222-2-2-2-2-2-2000000-2-222000000000000000000000000000000
χ36222222222222-22-22-2-2-2-2-22-2222-2-200000000-2-2-2-22222-2-200000022-2-2000000000000000000000000000000
χ37222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222000000000000000022002-22-20000002-22-2000000000000000000000000
χ38222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-22200000000000000002200-22-22000000-22-22000000000000000000000000
χ3922222222-2-2-2-22-22-2-2-2-2-22-22-222222222-2-2-2-200000000-2-2-2-200000000220000000000000000000000000000
χ4022222222-2-2-2-22-22-2-2-2-2-22-22-22222-2-2-2-2222200000000-2-22200000000-2-20000000000000000000000000000
χ4122222222-2-2-2-2-22-222222-22-22-2-2220000000022222222-2-2000000-2-2-2-2000000000000000000000000000000
χ4222222222-2-2-2-2-22-222222-22-22-2-22200000000-2-2-2-2-2-2-2-2-2-20000002222000000000000000000000000000000
χ4322222222-2-2-2-2-2-2-2-22222-2-2-2-222-2-2000000000000000022002-22-2000000-22-22000000000000000000000000
χ4422222222-2-2-2-2-2-2-2-22222-2-2-2-222-2-200000000000000002200-22-220000002-22-2000000000000000000000000
χ4522-2-22-2-222-22-220202-22-2-20-2000002i−2i2i−2i2i−2i2i−2i00000000000000000000000000i2−i2i2−i2i2−i2i2−i22−22−22−22−200000000
χ4622-2-22-2-222-22-220202-22-2-20-2000002i−2i2i−2i2i−2i2i−2i00000000000000000000000000−i2i2−i2i2−i2i2−i2i2−22−22−22−2200000000
χ4722-2-22-2-222-22-220202-22-2-20-200000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000i2−i2i2−i2i2−i2i2−i2−22−22−22−2200000000
χ4822-2-22-2-222-22-220202-22-2-20-200000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000−i2i2−i2i2−i2i2−i2i22−22−22−22−200000000
χ4922-2-22-2-22-22-222020-22-22-20-2000002i−2i2i−2i−2i2i−2i2i00000000000000000000000000i2−i2i2−i2−i2i2−i2i22−22−2−22−2200000000
χ5022-2-22-2-22-22-222020-22-22-20-2000002i−2i2i−2i−2i2i−2i2i00000000000000000000000000−i2i2−i2i2i2−i2i2−i2−22−222−22−200000000
χ5122-2-22-2-22-22-222020-22-22-20-200000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000i2−i2i2−i2−i2i2−i2i2−22−222−22−200000000
χ5222-2-22-2-22-22-222020-22-22-20-200000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000−i2i2−i2i2i2−i2i2−i22−22−2−22−2200000000
χ532-22-222-2-22i2i−2i−2i2-2-222i2i−2i−2i2-2-22−2i2i−2i2i22-2-22i2i−2i−2i00000000-22-2200000000−2i2i0000000000000000000000000000
χ542-22-222-2-22i2i−2i−2i2-2-222i2i−2i−2i2-2-22−2i2i−2i2i-2-222−2i−2i2i2i00000000-222-2000000002i−2i0000000000000000000000000000
χ552-22-222-2-22i2i−2i−2i-222-2−2i−2i2i2i-222-22i−2i−2i2i0000000022-2-2−2i−2i2i2i-22000000-222i−2i000000000000000000000000000000
χ562-22-222-2-22i2i−2i−2i-222-2−2i−2i2i2i-222-22i−2i−2i2i00000000-2-2222i2i−2i−2i-220000002-2−2i2i000000000000000000000000000000
χ572-22-222-2-22i2i−2i−2i-2-222−2i−2i2i2i-2-222−2i2i2i−2i00000000000000002-2002-2-220000002i−2i−2i2i000000000000000000000000
χ582-22-222-2-22i2i−2i−2i-2-222−2i−2i2i2i-2-222−2i2i2i−2i00000000000000002-200-222-2000000−2i2i2i−2i000000000000000000000000
χ592-22-222-2-2−2i−2i2i2i2-2-22−2i−2i2i2i2-2-222i−2i2i−2i22-2-2−2i−2i2i2i00000000-22-22000000002i−2i0000000000000000000000000000
χ602-22-222-2-2−2i−2i2i2i2-2-22−2i−2i2i2i2-2-222i−2i2i−2i-2-2222i2i−2i−2i00000000-222-200000000−2i2i0000000000000000000000000000
χ612-22-222-2-2−2i−2i2i2i-222-22i2i−2i−2i-222-2−2i2i2i−2i0000000022-2-22i2i−2i−2i-22000000-22−2i2i000000000000000000000000000000
χ622-22-222-2-2−2i−2i2i2i-222-22i2i−2i−2i-222-2−2i2i2i−2i00000000-2-222−2i−2i2i2i-220000002-22i−2i000000000000000000000000000000
χ632-22-222-2-2−2i−2i2i2i-2-2222i2i−2i−2i-2-2222i−2i−2i2i00000000000000002-2002-2-22000000−2i2i2i−2i000000000000000000000000
χ642-22-222-2-2−2i−2i2i2i-2-2222i2i−2i−2i-2-2222i−2i−2i2i00000000000000002-200-222-20000002i−2i−2i2i000000000000000000000000
χ652-2-222-22-22i−2i−2i2i20-202i−2i−2i2i-202000002i−2i−2i2i-222-200000000000000000000000000i2−i2−i2i2−222−22−2−22i2−i2−i2i200000000
χ662-2-222-22-22i−2i−2i2i20-202i−2i−2i2i-202000002i−2i−2i2i-222-200000000000000000000000000−i2i2i2−i22−2−22−222−2−i2i2i2−i200000000
χ672-2-222-22-22i−2i−2i2i20-202i−2i−2i2i-20200000−2i2i2i−2i2-2-2200000000000000000000000000i2−i2−i2i2−222−2−222−2−i2i2i2−i200000000
χ682-2-222-22-22i−2i−2i2i20-202i−2i−2i2i-20200000−2i2i2i−2i2-2-2200000000000000000000000000−i2i2i2−i22−2−222−2−22i2−i2−i2i200000000
χ692-2-222-22-2−2i2i2i−2i20-20−2i2i2i−2i-202000002i−2i−2i2i2-2-2200000000000000000000000000i2−i2−i2i22−2−222−2−22−i2i2i2−i200000000
χ702-2-222-22-2−2i2i2i−2i20-20−2i2i2i−2i-202000002i−2i−2i2i2-2-2200000000000000000000000000−i2i2i2−i2−222−2−222−2i2−i2−i2i200000000
χ712-2-222-22-2−2i2i2i−2i20-20−2i2i2i−2i-20200000−2i2i2i−2i-222-200000000000000000000000000i2−i2−i2i22−2−22−222−2i2−i2−i2i200000000
χ722-2-222-22-2−2i2i2i−2i20-20−2i2i2i−2i-20200000−2i2i2i−2i-222-200000000000000000000000000−i2i2i2−i2−222−22−2−22−i2i2i2−i200000000
χ7344-44-44-4-40000040400000-40-40000000000004-44-40000000000000000000000000000000000000000000000
χ7444-44-44-4-40000040400000-40-4000000000000-44-440000000000000000000000000000000000000000000000
χ7544-44-44-4-400000-40-40000040400000000000000004i−4i4i−4i000000000000000000000000000000000000000000
χ7644-44-44-4-400000-40-4000004040000000000000000−4i4i−4i4i000000000000000000000000000000000000000000
χ7744-4-44-4-444-44-4-40-40-44-44404000000000000000000000000000000000000000000000000000000000000000
χ7844-4-44-4-44-44-44-40-404-44-4404000000000000000000000000000000000000000000000000000000000000000
χ794-4-444-44-44i−4i−4i4i-4040−4i4i4i−4i40-4000000000000000000000000000000000000000000000000000000000000000
χ804-4-444-44-4−4i4i4i−4i-40404i−4i−4i4i40-4000000000000000000000000000000000000000000000000000000000000000
χ814-4-4-4-44440000040-400000-4040000000000004-4-440000000000000000000000000000000000000000000000
χ824-4-4-4-44440000040-400000-404000000000000-444-40000000000000000000000000000000000000000000000
χ834-4-4-4-444400000-4040000040-400000000000000004-4-44000000000000000000000000000000000000000000
χ844-4-4-4-444400000-4040000040-40000000000000000-444-4000000000000000000000000000000000000000000
χ85888-8-8-88-8000000000000000000000000000000000000000000000000000000000000000000000000000000
χ868-888-8-8-88000000000000000000000000000000000000000000000000000000000000000000000000000000

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