Finite Group Databasebeta

← Group #210104

Character table — Group #210104

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1111111122222222222222224444444444444444444444888888888888888888888888888888881616161616161616
order12222222444444444444444444444444444444444444442244444444444444888888888888888822448888
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
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ511111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ811111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ911111111-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1
χ1011111111-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111
χ1111111111-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ1211111111-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ1311111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-111
χ1411111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-111-1-1
χ1511111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ1611111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111
χ1711-1-111-1-1ii−i−i11-1-1ii−i−i11-1-1i−i11-1-1ii−i−ii−i11-1-1ii−i−i1-11-1i−i1-1i−i11-1-1ii−i−i11-1-1ii−i−i11-1-1ii−i−i1-1i−i1-1i−i
χ1811-1-111-1-1ii−i−i11-1-1ii−i−i11-1-1i−i11-1-1ii−i−ii−i11-1-1ii−i−i1-11-1i−i1-1i−i11-1-1ii−i−i-1-111−i−iii-1-111−i−iii-11−ii-11−ii
χ1911-1-111-1-1ii−i−i11-1-1ii−i−i11-1-1i−i11-1-1ii−i−ii−i-1-111−i−iii1-1-11−ii1-1i−i-1-111−i−iii11-1-1ii−i−i-1-111−i−iii1-1i−i-11−ii
χ2011-1-111-1-1ii−i−i11-1-1ii−i−i11-1-1i−i11-1-1ii−i−ii−i-1-111−i−iii1-1-11−ii1-1i−i-1-111−i−iii-1-111−i−iii11-1-1ii−i−i-11−ii1-1i−i
χ2111-1-111-1-1ii−i−i11-1-1ii−i−i11-1-1i−i-1-111−i−iiii−i11-1-1ii−i−i1-11-1i−i-11−ii-1-111−i−iii11-1-1ii−i−i11-1-1ii−i−i-11−ii-11−ii
χ2211-1-111-1-1ii−i−i11-1-1ii−i−i11-1-1i−i-1-111−i−iiii−i11-1-1ii−i−i1-11-1i−i-11−ii-1-111−i−iii-1-111−i−iii-1-111−i−iii1-1i−i1-1i−i
χ2311-1-111-1-1ii−i−i11-1-1ii−i−i11-1-1i−i-1-111−i−iiii−i-1-111−i−iii1-1-11−ii-11−ii11-1-1ii−i−i11-1-1ii−i−i-1-111−i−iii-11−ii1-1i−i
χ2411-1-111-1-1ii−i−i11-1-1ii−i−i11-1-1i−i-1-111−i−iiii−i-1-111−i−iii1-1-11−ii-11−ii11-1-1ii−i−i-1-111−i−iii11-1-1ii−i−i1-1i−i-11−ii
χ2511-1-111-1-1−i−iii11-1-1−i−iii11-1-1−ii11-1-1−i−iii−ii11-1-1−i−iii1-11-1−ii1-1−ii11-1-1−i−iii11-1-1−i−iii11-1-1−i−iii1-1−ii1-1−ii
χ2611-1-111-1-1−i−iii11-1-1−i−iii11-1-1−ii11-1-1−i−iii−ii11-1-1−i−iii1-11-1−ii1-1−ii11-1-1−i−iii-1-111ii−i−i-1-111ii−i−i-11i−i-11i−i
χ2711-1-111-1-1−i−iii11-1-1−i−iii11-1-1−ii11-1-1−i−iii−ii-1-111ii−i−i1-1-11i−i1-1−ii-1-111ii−i−i11-1-1−i−iii-1-111ii−i−i1-1−ii-11i−i
χ2811-1-111-1-1−i−iii11-1-1−i−iii11-1-1−ii11-1-1−i−iii−ii-1-111ii−i−i1-1-11i−i1-1−ii-1-111ii−i−i-1-111ii−i−i11-1-1−i−iii-11i−i1-1−ii
χ2911-1-111-1-1−i−iii11-1-1−i−iii11-1-1−ii-1-111ii−i−i−ii11-1-1−i−iii1-11-1−ii-11i−i-1-111ii−i−i11-1-1−i−iii11-1-1−i−iii-11i−i-11i−i
χ3011-1-111-1-1−i−iii11-1-1−i−iii11-1-1−ii-1-111ii−i−i−ii11-1-1−i−iii1-11-1−ii-11i−i-1-111ii−i−i-1-111ii−i−i-1-111ii−i−i1-1−ii1-1−ii
χ3111-1-111-1-1−i−iii11-1-1−i−iii11-1-1−ii-1-111ii−i−i−ii-1-111ii−i−i1-1-11i−i-11i−i11-1-1−i−iii11-1-1−i−iii-1-111ii−i−i-11i−i1-1−ii
χ3211-1-111-1-1−i−iii11-1-1−i−iii11-1-1−ii-1-111ii−i−i−ii-1-111ii−i−i1-1-11i−i-11i−i11-1-1−i−iii-1-111ii−i−i11-1-1−i−iii1-1−ii-11i−i
χ332222222222222-22-222222-22-2-2-200000000-2-222222222-2-2-2-2-2-2000000000000000000000000000000000000
χ342222222222222-22-222222-22-2-2-200000000-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000000000000
χ35222222222222-22-22-2-2-2-2-22-22-2-2222222222200000000-2-20000-2-2-2-200000000000000000000000000000000
χ36222222222222-22-22-2-2-2-2-22-22-2-2-2-2-2-2-2-2-2-22200000000-2-20000222200000000000000000000000000000000
χ37222222222222-2-2-2-2-2-2-2-2-2-2-2-22200000000-2-20000000022000000002-22-22-22-2000000000000000000000000
χ38222222222222-2-2-2-2-2-2-2-2-2-2-2-22200000000-2-2000000002200000000-22-22-22-22000000000000000000000000
χ3922222222-2-2-2-22-22-2-2-2-2-22-22-22200000000222222-2-2-2-2-2-2-2-222000000000000000000000000000000000000
χ4022222222-2-2-2-22-22-2-2-2-2-22-22-2220000000022-2-2-2-22222-2-222-2-2000000000000000000000000000000000000
χ4122222222-2-2-2-2-22-222222-22-22222222-2-2-2-2-2-200000000-2-20000-2-22200000000000000000000000000000000
χ4222222222-2-2-2-2-22-222222-22-2222-2-2-2-22222-2-200000000-2-2000022-2-200000000000000000000000000000000
χ4322222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-200000000220000000022000000002-22-2-22-22000000000000000000000000
χ4422222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-20000000022000000002200000000-22-222-22-2000000000000000000000000
χ4522-2-222-2-22i2i−2i−2i2-2-222i2i−2i−2i2-2-22−2i2i00000000−2i2i22-2-22i2i−2i−2i-22-22−2i2i000000000000000000000000000000000000
χ4622-2-222-2-22i2i−2i−2i2-2-222i2i−2i−2i2-2-22−2i2i00000000−2i2i-2-222−2i−2i2i2i-222-22i−2i000000000000000000000000000000000000
χ4722-2-222-2-22i2i−2i−2i-222-2−2i−2i2i2i-222-2−2i2i22-2-22i2i−2i−2i2i−2i00000000-220000-22−2i2i00000000000000000000000000000000
χ4822-2-222-2-22i2i−2i−2i-222-2−2i−2i2i2i-222-2−2i2i-2-222−2i−2i2i2i2i−2i00000000-2200002-22i−2i00000000000000000000000000000000
χ4922-2-222-2-22i2i−2i−2i-2-222−2i−2i2i2i-2-2222i−2i00000000−2i2i000000002-2000000002-2-222i−2i−2i2i000000000000000000000000
χ5022-2-222-2-22i2i−2i−2i-2-222−2i−2i2i2i-2-2222i−2i00000000−2i2i000000002-200000000-222-2−2i2i2i−2i000000000000000000000000
χ5122-2-222-2-2−2i−2i2i2i2-2-22−2i−2i2i2i2-2-222i−2i000000002i−2i22-2-2−2i−2i2i2i-22-222i−2i000000000000000000000000000000000000
χ5222-2-222-2-2−2i−2i2i2i2-2-22−2i−2i2i2i2-2-222i−2i000000002i−2i-2-2222i2i−2i−2i-222-2−2i2i000000000000000000000000000000000000
χ5322-2-222-2-2−2i−2i2i2i-222-22i2i−2i−2i-222-22i−2i22-2-2−2i−2i2i2i−2i2i00000000-220000-222i−2i00000000000000000000000000000000
χ5422-2-222-2-2−2i−2i2i2i-222-22i2i−2i−2i-222-22i−2i-2-2222i2i−2i−2i−2i2i00000000-2200002-2−2i2i00000000000000000000000000000000
χ5522-2-222-2-2−2i−2i2i2i-2-2222i2i−2i−2i-2-222−2i2i000000002i−2i000000002-2000000002-2-22−2i2i2i−2i000000000000000000000000
χ5622-2-222-2-2−2i−2i2i2i-2-2222i2i−2i−2i-2-222−2i2i000000002i−2i000000002-200000000-222-22i−2i−2i2i000000000000000000000000
χ572-22-22-22-22i−2i2i−2i20-202i−2i2i−2i-20200000000000002i−2i2i−2i2-22-2000000000000000000i2−i2i2−i22−22−22−22−2i2−i2i2−i200000000
χ582-22-22-22-22i−2i2i−2i20-202i−2i2i−2i-20200000000000002i−2i2i−2i2-22-2000000000000000000−i2i2−i2i2−22−22−22−22−i2i2−i2i200000000
χ592-22-22-22-22i−2i2i−2i20-202i−2i2i−2i-2020000000000000−2i2i−2i2i-22-22000000000000000000i2−i2i2−i22−22−2−22−22−i2i2−i2i200000000
χ602-22-22-22-22i−2i2i−2i20-202i−2i2i−2i-2020000000000000−2i2i−2i2i-22-22000000000000000000−i2i2−i2i2−22−222−22−2i2−i2i2−i200000000
χ612-22-22-22-2−2i2i−2i2i20-20−2i2i−2i2i-20200000000000002i−2i2i−2i-22-22000000000000000000i2−i2i2−i2−22−222−22−2−i2i2−i2i200000000
χ622-22-22-22-2−2i2i−2i2i20-20−2i2i−2i2i-20200000000000002i−2i2i−2i-22-22000000000000000000−i2i2−i2i22−22−2−22−22i2−i2i2−i200000000
χ632-22-22-22-2−2i2i−2i2i20-20−2i2i−2i2i-2020000000000000−2i2i−2i2i2-22-2000000000000000000i2−i2i2−i2−22−22−22−22i2−i2i2−i200000000
χ642-22-22-22-2−2i2i−2i2i20-20−2i2i−2i2i-2020000000000000−2i2i−2i2i2-22-2000000000000000000−i2i2−i2i22−22−22−22−2−i2i2−i2i200000000
χ652-2-222-2-222-2-2220202-2-22-20-200000000000002i−2i−2i2i−2i2i2i−2i000000000000000000i2−i2−i2i2−i2i2i2−i22−2−222−2−2200000000
χ662-2-222-2-222-2-2220202-2-22-20-200000000000002i−2i−2i2i−2i2i2i−2i000000000000000000−i2i2i2−i2i2−i2−i2i2−222−2−222−200000000
χ672-2-222-2-222-2-2220202-2-22-20-20000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000i2−i2−i2i2−i2i2i2−i2−222−2−222−200000000
χ682-2-222-2-222-2-2220202-2-22-20-20000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000−i2i2i2−i2i2−i2−i2i22−2−222−2−2200000000
χ692-2-222-2-22-222-22020-222-2-20-200000000000002i−2i−2i2i2i−2i−2i2i000000000000000000i2−i2−i2i2i2−i2−i2i22−2−22−222−200000000
χ702-2-222-2-22-222-22020-222-2-20-200000000000002i−2i−2i2i2i−2i−2i2i000000000000000000−i2i2i2−i2−i2i2i2−i2−222−22−2−2200000000
χ712-2-222-2-22-222-22020-222-2-20-20000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000i2−i2−i2i2i2−i2−i2i2−222−22−2−2200000000
χ722-2-222-2-22-222-22020-222-2-20-20000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000−i2i2i2−i2−i2i2i2−i22−2−22−222−200000000
χ734-44-44-44-44i−4i4i−4i-4040−4i4i−4i4i40-4000000000000000000000000000000000000000000000000000000000000000
χ744-44-44-44-4−4i4i−4i4i-40404i−4i4i−4i40-4000000000000000000000000000000000000000000000000000000000000000
χ754-44-4-44-440000040400000-40-4004i−4i4i−4i00000000000000000000000000000000000000000000000000000000
χ764-44-4-44-440000040400000-40-400−4i4i−4i4i00000000000000000000000000000000000000000000000000000000
χ774-44-4-44-4400000-40-4000004040000004-44-40000000000000000000000000000000000000000000000000000
χ784-44-4-44-4400000-40-400000404000000-44-440000000000000000000000000000000000000000000000000000
χ794-4-444-4-444-4-44-40-40-444-4404000000000000000000000000000000000000000000000000000000000000000
χ804-4-444-4-44-444-4-40-404-4-44404000000000000000000000000000000000000000000000000000000000000000
χ814-4-44-444-40000040-400000-404004i−4i−4i4i00000000000000000000000000000000000000000000000000000000
χ824-4-44-444-40000040-400000-40400−4i4i4i−4i00000000000000000000000000000000000000000000000000000000
χ834-4-44-444-400000-4040000040-40000004i−4i−4i4i0000000000000000000000000000000000000000000000000000
χ844-4-44-444-400000-4040000040-4000000−4i4i4i−4i0000000000000000000000000000000000000000000000000000
χ858888-8-8-8-8000000000000000000000000000000000000000000000000000000000000000000000000000000
χ8688-8-8-8-888000000000000000000000000000000000000000000000000000000000000000000000000000000

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