Finite Group Databasebeta

← Group #210113

Character table — Group #210113

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1111111122222222222222224444444444444444444444888888888888888888888888888888881616161616161616
order12222222444444444444444444444444444444444444442244444444444444888888888888888844448888
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
χ3111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ611111111111111111111111111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ911111111-1-1-1-11111-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-111-1-1
χ1011111111-1-1-1-11111-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111-1-111
χ1111111111-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-111-1-11111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111
χ1211111111-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-111-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1
χ1311111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ1411111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ1511111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ1611111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-111
χ171-1-111-11-1ii−i−i11-1-1ii−i−i11-1-1i−iii−i−i11-1-1ii−i−i11-1-1i−i1-11-1i−ii−i1-111-1-1ii−i−i11-1-1ii−i−iii−i−i11-1-11-1i−ii−i1-1
χ181-1-111-11-1ii−i−i11-1-1ii−i−i11-1-1i−iii−i−i11-1-1ii−i−i11-1-1i−i1-11-1i−ii−i1-111-1-1ii−i−i-1-111−i−iii−i−iii-1-111-11−ii−ii-11
χ191-1-111-11-1ii−i−i11-1-1ii−i−i11-1-1i−iii−i−i-1-111−i−iii11-1-1i−i1-1-11−iii−i1-1-1-111−i−iii11-1-1ii−i−iii−i−i11-1-1-11−ii−ii-11
χ201-1-111-11-1ii−i−i11-1-1ii−i−i11-1-1i−iii−i−i-1-111−i−iii11-1-1i−i1-1-11−iii−i1-1-1-111−i−iii-1-111−i−iii−i−iii-1-1111-1i−ii−i1-1
χ211-1-111-11-1ii−i−i11-1-1ii−i−i11-1-1i−i−i−iii11-1-1ii−i−i-1-111i−i1-11-1i−i−ii-11-1-111−i−iii11-1-1ii−i−i−i−iii-1-1111-1i−i−ii-11
χ221-1-111-11-1ii−i−i11-1-1ii−i−i11-1-1i−i−i−iii11-1-1ii−i−i-1-111i−i1-11-1i−i−ii-11-1-111−i−iii-1-111−i−iiiii−i−i11-1-1-11−iii−i1-1
χ231-1-111-11-1ii−i−i11-1-1ii−i−i11-1-1i−i−i−iii-1-111−i−iii-1-111i−i1-1-11−ii−ii-1111-1-1ii−i−i11-1-1ii−i−i−i−iii-1-111-11−iii−i1-1
χ241-1-111-11-1ii−i−i11-1-1ii−i−i11-1-1i−i−i−iii-1-111−i−iii-1-111i−i1-1-11−ii−ii-1111-1-1ii−i−i-1-111−i−iiiii−i−i11-1-11-1i−i−ii-11
χ251-1-111-11-1−i−iii11-1-1−i−iii11-1-1−iiii−i−i11-1-1−i−iii-1-111−ii1-11-1−iii−i-11-1-111ii−i−i11-1-1−i−iiiii−i−i-1-1111-1−iii−i-11
χ261-1-111-11-1−i−iii11-1-1−i−iii11-1-1−iiii−i−i11-1-1−i−iii-1-111−ii1-11-1−iii−i-11-1-111ii−i−i-1-111ii−i−i−i−iii11-1-1-11i−i−ii1-1
χ271-1-111-11-1−i−iii11-1-1−i−iii11-1-1−iiii−i−i-1-111ii−i−i-1-111−ii1-1-11i−ii−i-1111-1-1−i−iii11-1-1−i−iiiii−i−i-1-111-11i−i−ii1-1
χ281-1-111-11-1−i−iii11-1-1−i−iii11-1-1−iiii−i−i-1-111ii−i−i-1-111−ii1-1-11i−ii−i-1111-1-1−i−iii-1-111ii−i−i−i−iii11-1-11-1−iii−i-11
χ291-1-111-11-1−i−iii11-1-1−i−iii11-1-1−ii−i−iii11-1-1−i−iii11-1-1−ii1-11-1−ii−ii1-111-1-1−i−iii11-1-1−i−iii−i−iii11-1-11-1−ii−ii1-1
χ301-1-111-11-1−i−iii11-1-1−i−iii11-1-1−ii−i−iii11-1-1−i−iii11-1-1−ii1-11-1−ii−ii1-111-1-1−i−iii-1-111ii−i−iii−i−i-1-111-11i−ii−i-11
χ311-1-111-11-1−i−iii11-1-1−i−iii11-1-1−ii−i−iii-1-111ii−i−i11-1-1−ii1-1-11i−i−ii1-1-1-111ii−i−i11-1-1−i−iii−i−iii11-1-1-11i−ii−i-11
χ321-1-111-11-1−i−iii11-1-1−i−iii11-1-1−ii−i−iii-1-111ii−i−i11-1-1−ii1-1-11i−i−ii1-1-1-111ii−i−i-1-111ii−i−iii−i−i-1-1111-1−ii−ii1-1
χ332222222222222-22-222222-22-2-2-22222000000002222-2-2-2-20000-2-2-2-200000000000000000000000000000000
χ342222222222222-22-222222-22-2-2-2-2-2-2-200000000-2-2-2-2-2-2-2-20000222200000000000000000000000000000000
χ35222222222222-22-22-2-2-2-2-22-22-2-2000022222222000022-2-2-2-2-2-2000000000000000000000000000000000000
χ36222222222222-22-22-2-2-2-2-22-22-2-20000-2-2-2-2-2-2-2-2000022-2-22222000000000000000000000000000000000000
χ37222222222222-2-2-2-2-2-2-2-2-2-2-2-2220000000000000000-2-222000000002-22-22-22-2000000000000000000000000
χ38222222222222-2-2-2-2-2-2-2-2-2-2-2-2220000000000000000-2-22200000000-22-22-22-22000000000000000000000000
χ3922222222-2-2-2-22-22-2-2-2-2-22-22-222222200000000-2-2-2-222-2-20000-2-22200000000000000000000000000000000
χ4022222222-2-2-2-22-22-2-2-2-2-22-22-222-2-2-2-200000000222222-2-2000022-2-200000000000000000000000000000000
χ4122222222-2-2-2-2-22-222222-22-222200002222-2-2-2-20000-2-2-2-2-2-222000000000000000000000000000000000000
χ4222222222-2-2-2-2-22-222222-22-22220000-2-2-2-222220000-2-2-2-222-2-2000000000000000000000000000000000000
χ4322222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-200000000000000002222000000002-22-2-22-22000000000000000000000000
χ4422222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-20000000000000000222200000000-22-222-22-2000000000000000000000000
χ4522-22-22-2-22-22-2-20-202-22-22020002i−2i2i−2i000000002i−2i2i−2i00000000000000000000i2−i2i2−i2i2−i2i2−i22−22−22−22−200000000
χ4622-22-22-2-22-22-2-20-202-22-22020002i−2i2i−2i000000002i−2i2i−2i00000000000000000000−i2i2−i2i2−i2i2−i2i2−22−22−22−2200000000
χ4722-22-22-2-22-22-2-20-202-22-2202000−2i2i−2i2i00000000−2i2i−2i2i00000000000000000000i2−i2i2−i2i2−i2i2−i2−22−22−22−2200000000
χ4822-22-22-2-22-22-2-20-202-22-2202000−2i2i−2i2i00000000−2i2i−2i2i00000000000000000000−i2i2−i2i2−i2i2−i2i22−22−22−22−200000000
χ4922-22-22-2-2-22-22-20-20-22-222020002i−2i2i−2i00000000−2i2i−2i2i00000000000000000000i2−i2i2−i2−i2i2−i2i22−22−2−22−2200000000
χ5022-22-22-2-2-22-22-20-20-22-222020002i−2i2i−2i00000000−2i2i−2i2i00000000000000000000−i2i2−i2i2i2−i2i2−i2−22−222−22−200000000
χ5122-22-22-2-2-22-22-20-20-22-22202000−2i2i−2i2i000000002i−2i2i−2i00000000000000000000i2−i2i2−i2−i2i2−i2i2−22−222−22−200000000
χ5222-22-22-2-2-22-22-20-20-22-22202000−2i2i−2i2i000000002i−2i2i−2i00000000000000000000−i2i2−i2i2i2−i2i2−i22−22−2−22−2200000000
χ532-222-2-2-222i−2i−2i2i-20202i−2i−2i2i20-20002-2-2200000000−2i2i2i−2i00000000000000000000i2−i2−i2i2−222−2−i2i2i2−i2−222−200000000
χ542-222-2-2-222i−2i−2i2i-20202i−2i−2i2i20-20002-2-2200000000−2i2i2i−2i00000000000000000000−i2i2i2−i22−2−22i2−i2−i2i22−2−2200000000
χ552-222-2-2-222i−2i−2i2i-20202i−2i−2i2i20-2000-222-2000000002i−2i−2i2i00000000000000000000i2−i2−i2i2−222−2i2−i2−i2i22−2−2200000000
χ562-222-2-2-222i−2i−2i2i-20202i−2i−2i2i20-2000-222-2000000002i−2i−2i2i00000000000000000000−i2i2i2−i22−2−22−i2i2i2−i2−222−200000000
χ572-222-2-2-22−2i2i2i−2i-2020−2i2i2i−2i20-20002-2-22000000002i−2i−2i2i00000000000000000000i2−i2−i2i22−2−22−i2i2i2−i22−2−2200000000
χ582-222-2-2-22−2i2i2i−2i-2020−2i2i2i−2i20-20002-2-22000000002i−2i−2i2i00000000000000000000−i2i2i2−i2−222−2i2−i2−i2i2−222−200000000
χ592-222-2-2-22−2i2i2i−2i-2020−2i2i2i−2i20-2000-222-200000000−2i2i2i−2i00000000000000000000i2−i2−i2i22−2−22i2−i2−i2i2−222−200000000
χ602-222-2-2-22−2i2i2i−2i-2020−2i2i2i−2i20-2000-222-200000000−2i2i2i−2i00000000000000000000−i2i2i2−i2−222−2−i2i2i2−i22−2−2200000000
χ612-2-222-22-22i2i−2i−2i2-2-222i2i−2i−2i2-2-22−2i2i2i2i−2i−2i0000000022-2-2−2i2i-220000−2i2i-2200000000000000000000000000000000
χ622-2-222-22-22i2i−2i−2i2-2-222i2i−2i−2i2-2-22−2i2i−2i−2i2i2i00000000-2-222−2i2i-2200002i−2i2-200000000000000000000000000000000
χ632-2-222-22-22i2i−2i−2i-222-2−2i−2i2i2i-222-2−2i2i000022-2-22i2i−2i−2i00002i−2i-22-22−2i2i000000000000000000000000000000000000
χ642-2-222-22-22i2i−2i−2i-222-2−2i−2i2i2i-222-2−2i2i0000-2-222−2i−2i2i2i00002i−2i-222-22i−2i000000000000000000000000000000000000
χ652-2-222-22-22i2i−2i−2i-2-222−2i−2i2i2i-2-2222i−2i0000000000000000−2i2i2-2000000002-2-222i−2i−2i2i000000000000000000000000
χ662-2-222-22-22i2i−2i−2i-2-222−2i−2i2i2i-2-2222i−2i0000000000000000−2i2i2-200000000-222-2−2i2i2i−2i000000000000000000000000
χ672-2-222-22-2−2i−2i2i2i2-2-22−2i−2i2i2i2-2-222i−2i2i2i−2i−2i00000000-2-2222i−2i-220000−2i2i2-200000000000000000000000000000000
χ682-2-222-22-2−2i−2i2i2i2-2-22−2i−2i2i2i2-2-222i−2i−2i−2i2i2i0000000022-2-22i−2i-2200002i−2i-2200000000000000000000000000000000
χ692-2-222-22-2−2i−2i2i2i-222-22i2i−2i−2i-222-22i−2i000022-2-2−2i−2i2i2i0000−2i2i-22-222i−2i000000000000000000000000000000000000
χ702-2-222-22-2−2i−2i2i2i-222-22i2i−2i−2i-222-22i−2i0000-2-2222i2i−2i−2i0000−2i2i-222-2−2i2i000000000000000000000000000000000000
χ712-2-222-22-2−2i−2i2i2i-2-2222i2i−2i−2i-2-222−2i2i00000000000000002i−2i2-2000000002-2-22−2i2i2i−2i000000000000000000000000
χ722-2-222-22-2−2i−2i2i2i-2-2222i2i−2i−2i-2-222−2i2i00000000000000002i−2i2-200000000-222-22i−2i−2i2i000000000000000000000000
χ7344-44-44-4-44-44-44040-44-44-40-4000000000000000000000000000000000000000000000000000000000000000
χ7444-44-44-4-4-44-4440404-44-4-40-4000000000000000000000000000000000000000000000000000000000000000
χ7544-4-44-4-440000040-400000-40400000000004i−4i4i−4i000000000000000000000000000000000000000000000000
χ7644-4-44-4-440000040-400000-4040000000000−4i4i−4i4i000000000000000000000000000000000000000000000000
χ7744-4-44-4-4400000-4040000040-40000004i−4i4i−4i0000000000000000000000000000000000000000000000000000
χ7844-4-44-4-4400000-4040000040-4000000−4i4i−4i4i0000000000000000000000000000000000000000000000000000
χ794-444-4-4-444i−4i−4i4i40-40−4i4i4i−4i-404000000000000000000000000000000000000000000000000000000000000000
χ804-444-4-4-44−4i4i4i−4i40-404i−4i−4i4i-404000000000000000000000000000000000000000000000000000000000000000
χ814-44-444-4-40000040400000-40-400000000004-4-44000000000000000000000000000000000000000000000000
χ824-44-444-4-40000040400000-40-40000000000-444-4000000000000000000000000000000000000000000000000
χ834-44-444-4-400000-40-4000004040000004i−4i−4i4i0000000000000000000000000000000000000000000000000000
χ844-44-444-4-400000-40-400000404000000−4i4i4i−4i0000000000000000000000000000000000000000000000000000
χ85888-8-8-88-8000000000000000000000000000000000000000000000000000000000000000000000000000000
χ868-8-8-8-8888000000000000000000000000000000000000000000000000000000000000000000000000000000

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