Finite Group Databasebeta

← Group #227320

Character table — Group #227320

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size11111111222222222222222244444444444444444444444444444488888888888888888888161616161616161616161616
order12222222444444448888888844444444448888888888888888888822444444444488888888224444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-1-1-111-1-1-1-1
χ411111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-11111
χ51111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1
χ61111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111
χ71111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ81111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ91111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ101111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-111-1-1-1-1111111-1-111-1-1-1-111
χ121111111111111111-1-1-1-1-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11111-1-1-1-11111-1-111-1-11111-1-1
χ131111111111111111-1-1-1-1-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111
χ141111111111111111-1-1-1-1-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-111-1-11111-1-1-1-111-1-111-1-111-1-1
χ151111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1111111-1-1
χ161111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1111111111111-1-1-1-1-1-111
χ171-11-1-111-111-1-111-1-1iiii−i−i−i−i-1ii−i−i11-1-11ii−i−iii−i−iii−i−i1111-1-1-1-11-1i−i1-1i−i1-1i−i11-1-1ii−i−i1-1i−i1-1i−i1-1i−i
χ181-11-1-111-111-1-111-1-1iiii−i−i−i−i-1ii−i−i11-1-11ii−i−iii−i−iii−i−i1111-1-1-1-11-1−ii-11−ii-11i−i11-1-1ii−i−i-11−ii-11−ii-11−ii
χ191-11-1-111-111-1-111-1-1iiii−i−i−i−i-1ii−i−i-1-1111ii−i−i−i−iii−i−iii-1-1-1-11111-11i−i1-1i−i1-1i−i11-1-1−i−iii1-1−ii-11i−i-11−ii
χ201-11-1-111-111-1-111-1-1iiii−i−i−i−i-1ii−i−i-1-1111ii−i−i−i−iii−i−iii-1-1-1-11111-11−ii-11−ii-11i−i11-1-1−i−iii-11i−i1-1−ii1-1i−i
χ211-11-1-111-111-1-111-1-1iiii−i−i−i−i-1−i−iii11-1-11ii−i−i−i−iii−i−iii-1-1-1-111111-1i−i1-1i−i1-1−ii-1-111ii−i−i-11i−i1-1−ii-11−ii
χ221-11-1-111-111-1-111-1-1iiii−i−i−i−i-1−i−iii11-1-11ii−i−i−i−iii−i−iii-1-1-1-111111-1−ii-11−ii-11−ii-1-111ii−i−i1-1−ii-11i−i1-1i−i
χ231-11-1-111-111-1-111-1-1iiii−i−i−i−i-1−i−iii-1-1111ii−i−iii−i−iii−i−i1111-1-1-1-1-11i−i1-1i−i1-1−ii-1-111−i−iii-11−ii-11−ii1-1i−i
χ241-11-1-111-111-1-111-1-1iiii−i−i−i−i-1−i−iii-1-1111ii−i−iii−i−iii−i−i1111-1-1-1-1-11−ii-11−ii-11−ii-1-111−i−iii1-1i−i1-1i−i-11−ii
χ251-11-1-111-111-1-111-1-1−i−i−i−iiiii-1ii−i−i11-1-11−i−iiiii−i−iii−i−i-1-1-1-111111-1i−i-11i−i-11i−i-1-111−i−iii1-1i−i-11−ii1-1−ii
χ261-11-1-111-111-1-111-1-1−i−i−i−iiiii-1ii−i−i11-1-11−i−iiiii−i−iii−i−i-1-1-1-111111-1−ii1-1−ii1-1i−i-1-111−i−iii-11−ii1-1i−i-11i−i
χ271-11-1-111-111-1-111-1-1−i−i−i−iiiii-1ii−i−i-1-1111−i−iii−i−iii−i−iii1111-1-1-1-1-11i−i-11i−i-11i−i-1-111ii−i−i1-1−ii1-1−ii-11i−i
χ281-11-1-111-111-1-111-1-1−i−i−i−iiiii-1ii−i−i-1-1111−i−iii−i−iii−i−iii1111-1-1-1-1-11−ii1-1−ii1-1i−i-1-111ii−i−i-11i−i-11i−i1-1−ii
χ291-11-1-111-111-1-111-1-1−i−i−i−iiiii-1−i−iii11-1-11−i−iii−i−iii−i−iii1111-1-1-1-11-1i−i-11i−i-11−ii11-1-1−i−iii-11i−i-11i−i-11i−i
χ301-11-1-111-111-1-111-1-1−i−i−i−iiiii-1−i−iii11-1-11−i−iii−i−iii−i−iii1111-1-1-1-11-1−ii1-1−ii1-1−ii11-1-1−i−iii1-1−ii1-1−ii1-1−ii
χ311-11-1-111-111-1-111-1-1−i−i−i−iiiii-1−i−iii-1-1111−i−iiiii−i−iii−i−i-1-1-1-11111-11i−i-11i−i-11−ii11-1-1ii−i−i-11−ii1-1i−i1-1−ii
χ321-11-1-111-111-1-111-1-1−i−i−i−iiiii-1−i−iii-1-1111−i−iiiii−i−iii−i−i-1-1-1-11111-11−ii1-1−ii1-1−ii11-1-1ii−i−i1-1i−i-11−ii-11i−i
χ33222222222-22-22-22-200000000-222222222-200002222-2-2-2-200000000-2-200000000-2-200000000000000000000
χ34222222222-22-22-22-200000000-22222-2-2-2-2-20000-2-2-2-22222000000002200000000-2-200000000000000000000
χ35222222222-22-22-22-200000000-2-2-2-2-22222-20000-2-2-2-2222200000000-2-2000000002200000000000000000000
χ36222222222-22-22-22-200000000-2-2-2-2-2-2-2-2-2-200002222-2-2-2-20000000022000000002200000000000000000000
χ3722222222-22-22-22-2222222222-200000000-2-2-2-2-20000000000000000002222-2-2-2-20000000000000000000000
χ3822222222-22-22-22-2222222222-200000000-2-2-2-2-2000000000000000000-2-2-2-222220000000000000000000000
χ3922222222-22-22-22-22-2-2-2-2-2-2-2-2-200000000-2222200000000000000000022-2-2-2-2220000000000000000000000
χ4022222222-22-22-22-22-2-2-2-2-2-2-2-2-200000000-22222000000000000000000-2-22222-2-20000000000000000000000
χ4122-22-22-2-220-20-2020i2i2−i2−i2i2i2−i2−i202-22-22i−2i2i−2i0i2−i2i2−i22i−2i2i−2i000022−2−222−2−2000000000000i2−i2i2−i22−22−2000000000000
χ4222-22-22-2-220-20-2020i2i2−i2−i2i2i2−i2−i202-22-2−2i2i−2i2i0i2−i2i2−i2−2i2i−2i2i0000−2−222−2−222000000000000i2−i2i2−i2−22−22000000000000
χ4322-22-22-2-220-20-2020i2i2−i2−i2i2i2−i2−i20-22-222i−2i2i−2i0i2−i2i2−i2−2i2i−2i2i0000−2−222−2−222000000000000−i2i2−i2i22−22−2000000000000
χ4422-22-22-2-220-20-2020i2i2−i2−i2i2i2−i2−i20-22-22−2i2i−2i2i0i2−i2i2−i22i−2i2i−2i000022−2−222−2−2000000000000−i2i2−i2i2−22−22000000000000
χ4522-22-22-2-220-20-2020−i2−i2i2i2−i2−i2i2i202-22-22i−2i2i−2i0−i2i2−i2i22i−2i2i−2i0000−2−222−2−222000000000000−i2i2−i2i2−22−22000000000000
χ4622-22-22-2-220-20-2020−i2−i2i2i2−i2−i2i2i202-22-2−2i2i−2i2i0−i2i2−i2i2−2i2i−2i2i000022−2−222−2−2000000000000−i2i2−i2i22−22−2000000000000
χ4722-22-22-2-220-20-2020−i2−i2i2i2−i2−i2i2i20-22-222i−2i2i−2i0−i2i2−i2i2−2i2i−2i2i000022−2−222−2−2000000000000i2−i2i2−i2−22−22000000000000
χ4822-22-22-2-220-20-2020−i2−i2i2i2−i2−i2i2i20-22-22−2i2i−2i2i0−i2i2−i2i22i−2i2i−2i0000−2−222−2−222000000000000i2−i2i2−i22−22−2000000000000
χ492-22-2-222-22-2-222-2-220000000022i2i−2i−2i22-2-2-200002i2i−2i−2i−2i−2i2i2i00000000-2200000000−2i2i00000000000000000000
χ502-22-2-222-22-2-222-2-220000000022i2i−2i−2i-2-222-20000−2i−2i2i2i2i2i−2i−2i000000002-200000000−2i2i00000000000000000000
χ512-22-2-222-22-2-222-2-22000000002−2i−2i2i2i22-2-2-20000−2i−2i2i2i2i2i−2i−2i00000000-22000000002i−2i00000000000000000000
χ522-22-2-222-22-2-222-2-22000000002−2i−2i2i2i-2-222-200002i2i−2i−2i−2i−2i2i2i000000002-2000000002i−2i00000000000000000000
χ532-22-2-222-2-222-2-222-22i2i2i2i−2i−2i−2i−2i200000000-2−2i−2i2i2i0000000000000000002i−2i2-2−2i2i-220000000000000000000000
χ542-22-2-222-2-222-2-222-22i2i2i2i−2i−2i−2i−2i200000000-2−2i−2i2i2i000000000000000000−2i2i-222i−2i2-20000000000000000000000
χ552-22-2-222-2-222-2-222-2−2i−2i−2i−2i2i2i2i2i200000000-22i2i−2i−2i0000000000000000002i−2i-22−2i2i2-20000000000000000000000
χ562-22-2-222-2-222-2-222-2−2i−2i−2i−2i2i2i2i2i200000000-22i2i−2i−2i000000000000000000−2i2i2-22i−2i-220000000000000000000000
χ572-2-2-222-222020-20-2022−2−2−2−22202i−2i−2i2i2i−2i−2i2i02−2−22-222-20000−2−22222−2−2000000000000−i2i2i2−i2−i2i2i2−i2000000000000
χ582-2-2-222-222020-20-2022−2−2−2−22202i−2i−2i2i−2i2i2i−2i02−2−222-2-22000022−2−2−2−222000000000000−i2i2i2−i2i2−i2−i2i2000000000000
χ592-2-2-222-222020-20-2022−2−2−2−2220−2i2i2i−2i2i−2i−2i2i02−2−222-2-22000022−2−2−2−222000000000000i2−i2−i2i2−i2i2i2−i2000000000000
χ602-2-2-222-222020-20-2022−2−2−2−2220−2i2i2i−2i−2i2i2i−2i02−2−22-222-20000−2−22222−2−2000000000000i2−i2−i2i2i2−i2−i2i2000000000000
χ612-2-2-222-222020-20-20−2−22222−2−202i−2i−2i2i2i−2i−2i2i0−222−2-222-2000022−2−2−2−222000000000000i2−i2−i2i2i2−i2−i2i2000000000000
χ622-2-2-222-222020-20-20−2−22222−2−202i−2i−2i2i−2i2i2i−2i0−222−22-2-220000−2−22222−2−2000000000000i2−i2−i2i2−i2i2i2−i2000000000000
χ632-2-2-222-222020-20-20−2−22222−2−20−2i2i2i−2i2i−2i−2i2i0−222−22-2-220000−2−22222−2−2000000000000−i2i2i2−i2i2−i2−i2i2000000000000
χ642-2-2-222-222020-20-20−2−22222−2−20−2i2i2i−2i−2i2i2i−2i0−222−2-222-2000022−2−2−2−222000000000000−i2i2i2−i2−i2i2i2−i2000000000000
χ6544444444-4-4-4-4-4-4-4-40000000040000000040000000000000000000000000000000000000000000000000000
χ66444-4-4-4-440000000022−2222−2222−2222−220000000000000000002i2−2i22i2−2i22i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000
χ67444-4-4-4-440000000022−2222−2222−2222−22000000000000000000−2i22i2−2i22i2−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000
χ68444-4-4-4-4400000000−2222−2222−2222−22220000000000000000002i2−2i22i2−2i2−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000
χ69444-4-4-4-4400000000−2222−2222−2222−2222000000000000000000−2i22i2−2i22i22i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000
χ7044-44-44-4-4-404040-402i22i2−2i2−2i22i22i2−2i2−2i20000000000−2i22i2−2i22i2000000000000000000000000000000000000000000000000
χ7144-44-44-4-4-404040-40−2i2−2i22i22i2−2i2−2i22i22i200000000002i2−2i22i2−2i2000000000000000000000000000000000000000000000000
χ7244-4-44-44-4040-40-4040000000000000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000
χ7344-4-44-44-4040-40-404000000000000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000
χ7444-4-44-44-40-404040-44i−4i−4i4i4i−4i−4i4i00000000000000000000000000000000000000000000000000000000000000
χ7544-4-44-44-40-404040-4−4i4i4i−4i−4i4i4i−4i00000000000000000000000000000000000000000000000000000000000000
χ764-4444-4-4-4000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000022−22−2222−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000
χ774-4444-4-4-4000000002i2−2i22i2−2i2−2i22i2−2i22i2000000000000000000−222222−222i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000
χ784-4444-4-4-400000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000022−22−22222i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000
χ794-4444-4-4-400000000−2i22i2−2i22i22i2−2i22i2−2i2000000000000000000−222222−22−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000
χ804-44-4-444-4-4-444-4-44400000000-40000000040000000000000000000000000000000000000000000000000000
χ814-4-44-4-44404040-40-40000000000000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000
χ824-4-44-4-44404040-40-4000000000000000000000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000
χ834-4-44-4-4440-40-404044-4-44-444-400000000000000000000000000000000000000000000000000000000000000
χ844-4-44-4-4440-40-40404-444-44-4-4400000000000000000000000000000000000000000000000000000000000000
χ854-4-4-444-44-40-4040402222−22−22−22−2222220000000000−222222−22000000000000000000000000000000000000000000000000
χ864-4-4-444-44-40-404040−22−2222222222−22−22000000000022−22−2222000000000000000000000000000000000000000000000000

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