Finite Group Databasebeta

← Group #222467

Character table — Group #222467

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222244444444444444444444444444888888888888888888888888888816161616161616161616
order12222222444444442222444444444488888888888822444444448888888888888888884444444488
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1
χ31111111111111111111111111-1-1-1-11111111111111-1-11111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111
χ511111111111111111111-1-1-1-11111111111-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1
χ611111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-111
χ711111111111111111111-1-1-1-11-1-1-1-111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111
χ811111111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1111111-1-11111-1-1-1-1111111-1-1-1-111-1-1
χ91111111111111111-1-1-1-111111111111111-1-1-1-111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ101111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111
χ111111111111111111-1-1-1-111111-1-1-1-111111-1-1-1-11111-1-111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ121111111111111111-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1111111111111-1-11111-1-1-1-1
χ131111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111
χ141111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111111111111111-1-1-1-1-1-111-1-111-1-1
χ151111111111111111-1-1-1-1-1-1-1-11-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1
χ161111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-11111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-111-1-111
χ171-1-1-11-111-1111-11-1-111-1-1ii−i−i111-1-1-111-1-1ii−i−i11-1-11-1i−i1-11-11-1ii−i−ii−iii−i−i11-1-1ii−i−ii−ii−i1-11-1i−i
χ181-1-1-11-111-1111-11-1-111-1-1ii−i−i111-1-1-1-1-111ii−i−i-1-111-11i−i1-11-1-11−i−iiii−iii−i−i-1-111−i−iiii−i−ii1-1-11−ii
χ191-1-1-11-111-1111-11-1-111-1-1ii−i−i1-1-111-111-1-1ii−i−i11-1-1-11i−i1-1-11-11ii−i−ii−i−i−iii11-1-1ii−i−i−ii−ii-11-11−ii
χ201-1-1-11-111-1111-11-1-111-1-1ii−i−i1-1-111-1-1-111ii−i−i-1-1111-1i−i1-1-111-1−i−iiii−i−i−iii-1-111−i−iii−iii−i-111-1i−i
χ211-1-1-11-111-1111-11-1-111-1-1−i−iii111-1-1-111-1-1−i−iii11-1-11-1−ii1-11-11-1−i−iii−ii−i−iii11-1-1−i−iii−ii−ii1-11-1−ii
χ221-1-1-11-111-1111-11-1-111-1-1−i−iii111-1-1-1-1-111−i−iii-1-111-11−ii1-11-1-11ii−i−i−ii−i−iii-1-111ii−i−i−iii−i1-1-11i−i
χ231-1-1-11-111-1111-11-1-111-1-1−i−iii1-1-111-111-1-1−i−iii11-1-1-11−ii1-1-11-11−i−iii−iiii−i−i11-1-1−i−iiii−ii−i-11-11i−i
χ241-1-1-11-111-1111-11-1-111-1-1−i−iii1-1-111-1-1-111−i−iii-1-1111-1−ii1-1-111-1ii−i−i−iiii−i−i-1-111ii−i−ii−i−ii-111-1−ii
χ251-1-1-11-111-1111-11-1-1-1-111ii−i−i111-1-1-111-1-1−i−iii11-1-11-1i−i-111-11-1ii−i−i−ii−i−iii-1-111−i−iiii−ii−i-11-11−ii
χ261-1-1-11-111-1111-11-1-1-1-111ii−i−i111-1-1-1-1-111−i−iii-1-111-11i−i-111-1-11−i−iii−ii−i−iii11-1-1ii−i−ii−i−ii-111-1i−i
χ271-1-1-11-111-1111-11-1-1-1-111ii−i−i1-1-111-111-1-1−i−iii11-1-1-11i−i-11-11-11ii−i−i−iiii−i−i-1-111−i−iii−ii−ii1-11-1i−i
χ281-1-1-11-111-1111-11-1-1-1-111ii−i−i1-1-111-1-1-111−i−iii-1-1111-1i−i-11-111-1−i−iii−iiii−i−i11-1-1ii−i−i−iii−i1-1-11−ii
χ291-1-1-11-111-1111-11-1-1-1-111−i−iii111-1-1-111-1-1ii−i−i11-1-11-1−ii-111-11-1−i−iiii−iii−i−i-1-111ii−i−i−ii−ii-11-11i−i
χ301-1-1-11-111-1111-11-1-1-1-111−i−iii111-1-1-1-1-111ii−i−i-1-111-11−ii-111-1-11ii−i−ii−iii−i−i11-1-1−i−iii−iii−i-111-1−ii
χ311-1-1-11-111-1111-11-1-1-1-111−i−iii1-1-111-111-1-1ii−i−i11-1-1-11−ii-11-11-11−i−iiii−i−i−iii-1-111ii−i−ii−ii−i1-11-1−ii
χ321-1-1-11-111-1111-11-1-1-1-111−i−iii1-1-111-1-1-111ii−i−i-1-1111-1−ii-11-111-1ii−i−ii−i−i−iii11-1-1−i−iiii−i−ii1-1-11i−i
χ33222222222-2-2222-2-200000000-22222-222220000-2-2-2-2220000-2-2-2-20000000000000000000000000000
χ34222222222-2-2222-2-200000000-22222-2-2-2-2-200002222-2-20000-2-2220000000000000000000000000000
χ35222222222-2-2222-2-200000000-2-2-2-2-2-222220000-2-2-2-2-2-2000022220000000000000000000000000000
χ36222222222-2-2222-2-200000000-2-2-2-2-2-2-2-2-2-20000222222000022-2-20000000000000000000000000000
χ3722222222-222-2-2-22222222222-20000-200002222000000-2-2-2-200000000-2-20000000000000000000000
χ3822222222-222-2-2-2222222-2-2-2-2-20000-20000-2-2-2-200000022-2-200000000220000000000000000000000
χ3922222222-222-2-2-222-2-2-2-22222-20000-20000-2-2-2-2000000-2-22200000000220000000000000000000000
χ4022222222-222-2-2-222-2-2-2-2-2-2-2-2-20000-200002222000000222200000000-2-20000000000000000000000
χ4122-2-2-222-202-20002-22-22-22-22-2000000i2−i2i2−i22-22-2i2−i2i2−i20000000000i2−i2i2−i2000000i2−i2i2−i2i2−i2i2−i20000000000
χ4222-2-2-222-202-20002-22-22-22-22-2000000−i2i2−i2i22-22-2−i2i2−i2i20000000000−i2i2−i2i2000000−i2i2−i2i2−i2i2−i2i20000000000
χ4322-2-2-222-202-20002-22-22-2-22-22000000i2−i2i2−i2-22-22i2−i2i2−i20000000000−i2i2−i2i2000000i2−i2i2−i2−i2i2−i2i20000000000
χ4422-2-2-222-202-20002-22-22-2-22-22000000−i2i2−i2i2-22-22−i2i2−i2i20000000000i2−i2i2−i2000000−i2i2−i2i2i2−i2i2−i20000000000
χ4522-2-2-222-202-20002-2-22-222-22-2000000i2−i2i2−i2-22-22i2−i2i2−i20000000000i2−i2i2−i2000000−i2i2−i2i2−i2i2−i2i20000000000
χ4622-2-2-222-202-20002-2-22-222-22-2000000−i2i2−i2i2-22-22−i2i2−i2i20000000000−i2i2−i2i2000000i2−i2i2−i2i2−i2i2−i20000000000
χ4722-2-2-222-202-20002-2-22-22-22-22000000i2−i2i2−i22-22-2i2−i2i2−i20000000000−i2i2−i2i2000000−i2i2−i2i2i2−i2i2−i20000000000
χ4822-2-2-222-202-20002-2-22-22-22-22000000−i2i2−i2i22-22-2−i2i2−i2i20000000000i2−i2i2−i2000000i2−i2i2−i2−i2i2−i2i20000000000
χ492-222-2-22-202-2000-222-2-222i−2i−2i2i000000i2−i2−i2i22i−2i−2i2ii2−i2−i2i20000000000−222−2000000i2−i2−i2i2−222−20000000000
χ502-222-2-22-202-2000-222-2-222i−2i−2i2i000000−i2i2i2−i22i−2i−2i2i−i2i2i2−i200000000002−2−22000000−i2i2i2−i22−2−220000000000
χ512-222-2-22-202-2000-222-2-22−2i2i2i−2i000000i2−i2−i2i2−2i2i2i−2ii2−i2−i2i200000000002−2−22000000i2−i2−i2i22−2−220000000000
χ522-222-2-22-202-2000-222-2-22−2i2i2i−2i000000−i2i2i2−i2−2i2i2i−2i−i2i2i2−i20000000000−222−2000000−i2i2i2−i2−222−20000000000
χ532-222-2-22-202-2000-22-222-22i−2i−2i2i000000i2−i2−i2i2−2i2i2i−2ii2−i2−i2i20000000000−222−2000000−i2i2i2−i22−2−220000000000
χ542-222-2-22-202-2000-22-222-22i−2i−2i2i000000−i2i2i2−i2−2i2i2i−2i−i2i2i2−i200000000002−2−22000000i2−i2−i2i2−222−20000000000
χ552-222-2-22-202-2000-22-222-2−2i2i2i−2i000000i2−i2−i2i22i−2i−2i2ii2−i2−i2i200000000002−2−22000000−i2i2i2−i2−222−20000000000
χ562-222-2-22-202-2000-22-222-2−2i2i2i−2i000000−i2i2i2−i22i−2i−2i2i−i2i2i2−i20000000000−222−2000000i2−i2−i2i22−2−220000000000
χ572-2-2-22-222222-22-2-2-222-2-22i2i−2i−2i-20000200002i2i−2i−2i000000−2i2i-2200000000−2i2i0000000000000000000000
χ582-2-2-22-222222-22-2-2-222-2-2−2i−2i2i2i-2000020000−2i−2i2i2i0000002i−2i-22000000002i−2i0000000000000000000000
χ592-2-2-22-222222-22-2-2-2-2-2222i2i−2i−2i-2000020000−2i−2i2i2i000000−2i2i2-2000000002i−2i0000000000000000000000
χ602-2-2-22-222222-22-2-2-2-2-222−2i−2i2i2i-20000200002i2i−2i−2i0000002i−2i2-200000000−2i2i0000000000000000000000
χ612-2-2-22-222-2-2-22-222200000000-222-2-2222-2-20000-2-2222-20000-22-220000000000000000000000000000
χ622-2-2-22-222-2-2-22-222200000000-222-2-22-2-222000022-2-2-220000-222-20000000000000000000000000000
χ632-2-2-22-222-2-2-22-222200000000-2-2-222222-2-20000-2-222-2200002-22-20000000000000000000000000000
χ642-2-2-22-222-2-2-22-222200000000-2-2-2222-2-222000022-2-22-200002-2-220000000000000000000000000000
χ6544444444-4-4-4-4-4-4-4-40000000040000400000000000000000000000000000000000000000000000000
χ6644-444-4-4-44004-4-40000000000000000000000000000000000000000000022−2222−22000000000000000000
χ6744-444-4-4-44004-4-400000000000000000000000000000000000000000000−2222−2222000000000000000000
χ6844-444-4-4-4-400-444000000000004i−4i4i−4i000000000000000000000000000000000000000000000000000
χ6944-444-4-4-4-400-44400000000000−4i4i−4i4i000000000000000000000000000000000000000000000000000
χ7044-4-4-444-40-44000-44000000000000002i2−2i22i2−2i20000−2i22i2−2i22i200000000000000000000000000000000000000
χ7144-4-4-444-40-44000-4400000000000000−2i22i2−2i22i200002i2−2i22i2−2i200000000000000000000000000000000000000
χ724-444-4-44-40-440004-4000000000000002i2−2i2−2i22i20000−2i22i22i2−2i200000000000000000000000000000000000000
χ734-444-4-44-40-440004-400000000000000−2i22i22i2−2i200002i2−2i2−2i22i200000000000000000000000000000000000000
χ744-44-444-4-4400-4-44000000000004i−4i−4i4i000000000000000000000000000000000000000000000000000
χ754-44-444-4-4400-4-4400000000000−4i4i4i−4i000000000000000000000000000000000000000000000000000
χ764-44-444-4-4-40044-4000000000000000000000000000000000000000000002i2−2i2−2i22i2000000000000000000
χ774-44-444-4-4-40044-400000000000000000000000000000000000000000000−2i22i22i2−2i2000000000000000000
χ784-4-4-44-4444-4-4-44-4440000000040000-400000000000000000000000000000000000000000000000000
χ79888-8-8-8-88000000000000000000000000000000000000000000000000000000000000000000000000
χ808-8-88-88-88000000000000000000000000000000000000000000000000000000000000000000000000

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