Finite Group Databasebeta

← Group #209803

Character table — Group #209803

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111111122222222222244444444444444448888888888888888888888888888888888881616161616161616
order12222222444444444444444444444444444422224444444444444444888888888888888844448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ5111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ6111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ7111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ91111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-111-1-1
χ101111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-111-1-111
χ111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-111-1-11111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ121111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ131111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1111111-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ141111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111
χ151111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-11111-1-1-1-1-1-111-1-111
χ161111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-11111-1-1-1-1111111-1-111-1-1
χ1711-11-1-11-11-1ii−i−i1-11-11-1ii−i−i11-1-1ii−i−ii−i1-111-1-11-1i−i1-1i−ii−iii−i−i1-1ii−i−i11-1-1ii−i−i11-1-1i−i1-1i−i1-1
χ1811-11-1-11-11-1ii−i−i1-11-11-1ii−i−i11-1-1ii−i−ii−i1-111-1-11-1i−i1-1i−ii−iii−i−i1-1−i−iii-1-111−i−iii-1-111−ii-11−ii-11
χ1911-11-1-11-11-1ii−i−i1-11-11-1ii−i−i11-1-1ii−i−ii−i1-1-1-1111-1−ii-11−iii−i−i−iii-11ii−i−i11-1-1−i−iii-1-111i−i1-1−ii-11
χ2011-11-1-11-11-1ii−i−i1-11-11-1ii−i−i11-1-1ii−i−ii−i1-1-1-1111-1−ii-11−iii−i−i−iii-11−i−iii-1-111ii−i−i11-1-1−ii-11i−i1-1
χ2111-11-1-11-11-1ii−i−i1-11-11-1ii−i−i-1-111−i−iiii−i1-111-1-1-11−ii-11−ii−iiii−i−i-11ii−i−i11-1-1−i−iii-1-111−ii-11i−i1-1
χ2211-11-1-11-11-1ii−i−i1-11-11-1ii−i−i-1-111−i−iiii−i1-111-1-1-11−ii-11−ii−iiii−i−i-11−i−iii-1-111ii−i−i11-1-1i−i1-1−ii-11
χ2311-11-1-11-11-1ii−i−i1-11-11-1ii−i−i-1-111−i−iiii−i1-1-1-111-11i−i1-1i−i−ii−i−iii1-1ii−i−i11-1-1ii−i−i11-1-1−ii-11−ii-11
χ2411-11-1-11-11-1ii−i−i1-11-11-1ii−i−i-1-111−i−iiii−i1-1-1-111-11i−i1-1i−i−ii−i−iii1-1−i−iii-1-111−i−iii-1-111i−i1-1i−i1-1
χ2511-11-1-11-11-1−i−iii1-11-11-1−i−iii11-1-1−i−iii−ii1-111-1-11-1−ii1-1−ii−ii−i−iii1-1ii−i−i-1-111ii−i−i-1-111i−i-11i−i-11
χ2611-11-1-11-11-1−i−iii1-11-11-1−i−iii11-1-1−i−iii−ii1-111-1-11-1−ii1-1−ii−ii−i−iii1-1−i−iii11-1-1−i−iii11-1-1−ii1-1−ii1-1
χ2711-11-1-11-11-1−i−iii1-11-11-1−i−iii11-1-1−i−iii−ii1-1-1-1111-1i−i-11i−i−iiii−i−i-11ii−i−i-1-111−i−iii11-1-1i−i-11−ii1-1
χ2811-11-1-11-11-1−i−iii1-11-11-1−i−iii11-1-1−i−iii−ii1-1-1-1111-1i−i-11i−i−iiii−i−i-11−i−iii11-1-1ii−i−i-1-111−ii1-1i−i-11
χ2911-11-1-11-11-1−i−iii1-11-11-1−i−iii-1-111ii−i−i−ii1-111-1-1-11i−i-11i−ii−i−i−iii-11ii−i−i-1-111−i−iii11-1-1−ii1-1i−i-11
χ3011-11-1-11-11-1−i−iii1-11-11-1−i−iii-1-111ii−i−i−ii1-111-1-1-11i−i-11i−ii−i−i−iii-11−i−iii11-1-1ii−i−i-1-111i−i-11−ii1-1
χ3111-11-1-11-11-1−i−iii1-11-11-1−i−iii-1-111ii−i−i−ii1-1-1-111-11−ii1-1−iii−iii−i−i1-1ii−i−i-1-111ii−i−i-1-111−ii1-1−ii1-1
χ3211-11-1-11-11-1−i−iii1-11-11-1−i−iii-1-111ii−i−i−ii1-1-1-111-11−ii1-1−iii−iii−i−i1-1−i−iii11-1-1−i−iii11-1-1i−i-11i−i-11
χ3322222222222222-2-222-2-22-22-22222-2-2-2-2-2-2-2-20000-2-200000022000000000000000000000000000000
χ3422222222222222-2-222-2-22-22-2-2-2-2-22222-2-2-2-2000022000000-2-2000000000000000000000000000000
χ352222222222-2-2-2-2-2-222-2-2-22-222222222222-2-20000-2-2000000-2-2000000000000000000000000000000
χ362222222222-2-2-2-2-2-222-2-2-22-22-2-2-2-2-2-2-2-222-2-200002200000022000000000000000000000000000000
χ3722222222-2-2222222-2-222-22-2200000000-2-2-2-20000002222-2-2000000-2-2000000000000000000000000
χ3822222222-2-2222222-2-222-22-2200000000-2-2-2-2000000-2-2-2-22200000022000000000000000000000000
χ3922222222-2-22222-2-2-2-2-2-2-2-2-2-20000000022222-22-200000000002-22-200000000000000000000000000
χ4022222222-2-22222-2-2-2-2-2-2-2-2-2-2000000002222-22-220000000000-22-2200000000000000000000000000
χ4122222222-2-2-2-2-2-222-2-2222-22-20000000022-2-200000022-2-2-2-200000022000000000000000000000000
χ4222222222-2-2-2-2-2-222-2-2222-22-20000000022-2-2000000-2-22222000000-2-2000000000000000000000000
χ4322222222-2-2-2-2-2-2-2-2-2-2-2-2222200000000-2-2222-22-20000000000-22-2200000000000000000000000000
χ4422222222-2-2-2-2-2-2-2-2-2-2-2-2222200000000-2-222-22-2200000000002-22-200000000000000000000000000
χ4522-22-2-22-22-22i2i−2i−2i-222-2-222i−2i−2i2i22-2-2−2i−2i2i2i−2i2i-220000-220000002i−2i000000000000000000000000000000
χ4622-22-2-22-22-22i2i−2i−2i-222-2-222i−2i−2i2i-2-2222i2i−2i−2i−2i2i-2200002-2000000−2i2i000000000000000000000000000000
χ4722-22-2-22-22-2−2i−2i2i2i-222-2-22−2i2i2i−2i22-2-22i2i−2i−2i2i−2i-220000-22000000−2i2i000000000000000000000000000000
χ4822-22-2-22-22-2−2i−2i2i2i-222-2-22−2i2i2i−2i-2-222−2i−2i2i2i2i−2i-2200002-20000002i−2i000000000000000000000000000000
χ4922-22-2-22-2-222i2i−2i−2i2-2-222-2−2i2i2i−2i00000000−2i2i-220000002i−2i2-2−2i2i000000-22000000000000000000000000
χ5022-22-2-22-2-222i2i−2i−2i2-2-222-2−2i2i2i−2i00000000−2i2i-22000000−2i2i-222i−2i0000002-2000000000000000000000000
χ5122-22-2-22-2-222i2i−2i−2i-22-22-22−2i−2i2i2i000000002i−2i2-22-2-2200000000002i−2i−2i2i00000000000000000000000000
χ5222-22-2-22-2-222i2i−2i−2i-22-22-22−2i−2i2i2i000000002i−2i2-2-222-20000000000−2i2i2i−2i00000000000000000000000000
χ5322-22-2-22-2-22−2i−2i2i2i2-2-222-22i−2i−2i2i000000002i−2i-220000002i−2i-22−2i2i0000002-2000000000000000000000000
χ5422-22-2-22-2-22−2i−2i2i2i2-2-222-22i−2i−2i2i000000002i−2i-22000000−2i2i2-22i−2i000000-22000000000000000000000000
χ5522-22-2-22-2-22−2i−2i2i2i-22-22-222i2i−2i−2i00000000−2i2i2-22-2-220000000000−2i2i2i−2i00000000000000000000000000
χ5622-22-2-22-2-22−2i−2i2i2i-22-22-222i2i−2i−2i00000000−2i2i2-2-222-200000000002i−2i−2i2i00000000000000000000000000
χ57444-44-4-4-444000000-4-400000000004-44-4000000000000000000000000000000000000000000000000
χ58444-44-4-4-444000000-4-40000000000-44-44000000000000000000000000000000000000000000000000
χ59444-44-4-4-4-4-4000000440000004i−4i4i−4i0000000000000000000000000000000000000000000000000000
χ60444-44-4-4-4-4-400000044000000−4i4i−4i4i0000000000000000000000000000000000000000000000000000
χ6144-4-4-44-444-4000000-4400000000004i−4i−4i4i000000000000000000000000000000000000000000000000
χ6244-4-4-44-444-4000000-440000000000−4i4i4i−4i000000000000000000000000000000000000000000000000
χ6344-4-4-44-44-440000004-40000004i−4i−4i4i0000000000000000000000000000000000000000000000000000
χ6444-4-4-44-44-440000004-4000000−4i4i4i−4i0000000000000000000000000000000000000000000000000000
χ654-444-4-4-44004-44-4000000000000000000000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i00000000
χ664-444-4-4-44004-44-400000000000000000000000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i00000000
χ674-444-4-4-4400-44-44000000000000000000000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i00000000
χ684-444-4-4-4400-44-4400000000000000000000000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i00000000
χ694-44-4-444-40000004-400-4400000000000000000000000000000000000000002i2−2i22i2−2i20000000000000000
χ704-44-4-444-40000004-400-440000000000000000000000000000000000000000−2i22i2−2i22i20000000000000000
χ714-44-4-444-4000000-44004-40000000000000000000000000000000000002i2−2i22i2−2i200000000000000000000
χ724-44-4-444-4000000-44004-4000000000000000000000000000000000000−2i22i2−2i22i200000000000000000000
χ734-4-4444-4-4004i−4i−4i4i000000000000000000000000000000000000000000000000002-2-22−2i2i2i−2i00000000
χ744-4-4444-4-4004i−4i−4i4i00000000000000000000000000000000000000000000000000-222-22i−2i−2i2i00000000
χ754-4-4444-4-400−4i4i4i−4i000000000000000000000000000000000000000000000000002-2-222i−2i−2i2i00000000
χ764-4-4444-4-400−4i4i4i−4i00000000000000000000000000000000000000000000000000-222-2−2i2i2i−2i00000000
χ774-4-4-44-4440000004400-4-400000000000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ784-4-4-44-4440000004400-4-40000000000000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ794-4-4-44-444000000-4-4004400000000000000000000000000000000000022−22−222200000000000000000000
χ804-4-4-44-444000000-4-40044000000000000000000000000000000000000−222222−2200000000000000000000

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