Finite Group Databasebeta

← Group #222512

Character table — Group #222512

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222244444444444444444444444444888888888888888888888888888816161616161616161616
order12222222444444442222222244444488888888888844444444448888888888888888882244444488
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1
χ31111111111111111111111111-1-1-1-111111-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-1
χ41111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111
χ511111111111111111111-1-1-1-111111111111111111111-1-1-1-111-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111
χ711111111111111111111-1-1-1-11-1-1-1-111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-111
χ811111111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-11111-1-1-1-11111-1-1
χ91111111111111111-1-1-1-111111111111111-1-1-1-11111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ101111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111
χ111111111111111111-1-1-1-111111-1-1-1-11111111111111-1-11111-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111
χ121111111111111111-1-1-1-111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-111111111111111-1-1-1-1-1-111-1-111-1-1
χ131111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111
χ141111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1
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
χ161111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-11111-1-1-1-111-1-111-1-111
χ171-1-111-1-1111-11-1-1-1111-1-111-1-11ii−i−i-111-1-1ii−i−i11-1-1i−i1-11-11-11-1ii−i−ii−iii−i−i11-1-1ii−i−i1-1i−ii−i1-1i−i
χ181-1-111-1-1111-11-1-1-1111-1-111-1-11ii−i−i-1-1-111ii−i−i-1-111i−i1-1-111-1-11−i−iiii−iii−i−i-1-111−i−iii1-1−iii−i-11−ii
χ191-1-111-1-1111-11-1-1-1111-1-111-1-11−i−iii-111-1-1−i−iii11-1-1−ii1-11-11-11-1−i−iii−ii−i−iii11-1-1−i−iii1-1−ii−ii1-1−ii
χ201-1-111-1-1111-11-1-1-1111-1-111-1-11−i−iii-1-1-111−i−iii-1-111−ii1-1-111-1-11ii−i−i−ii−i−iii-1-111ii−i−i1-1i−i−ii-11i−i
χ211-1-111-1-1111-11-1-1-1111-1-1-1-1111ii−i−i-111-1-1ii−i−i11-1-1i−i-11-111-1-11ii−i−ii−i−i−iii11-1-1ii−i−i-11−ii−ii-11−ii
χ221-1-111-1-1111-11-1-1-1111-1-1-1-1111ii−i−i-1-1-111ii−i−i-1-111i−i-111-11-11-1−i−iiii−i−i−iii-1-111−i−iii-11i−i−ii1-1i−i
χ231-1-111-1-1111-11-1-1-1111-1-1-1-1111−i−iii-111-1-1−i−iii11-1-1−ii-11-111-1-11−i−iii−iiii−i−i11-1-1−i−iii-11i−ii−i-11i−i
χ241-1-111-1-1111-11-1-1-1111-1-1-1-1111−i−iii-1-1-111−i−iii-1-111−ii-111-11-11-1ii−i−i−iiii−i−i-1-111ii−i−i-11−iii−i1-1−ii
χ251-1-111-1-1111-11-1-1-11-1-11111-1-11ii−i−i-111-1-1−i−iii11-1-1i−i1-11-1-111-1ii−i−i−ii−i−iii-1-111−i−iii-11i−ii−i-11−ii
χ261-1-111-1-1111-11-1-1-11-1-11111-1-11ii−i−i-1-1-111−i−iii-1-111i−i1-1-11-11-11−i−iii−ii−i−iii11-1-1ii−i−i-11−iii−i1-1i−i
χ271-1-111-1-1111-11-1-1-11-1-11111-1-11−i−iii-111-1-1ii−i−i11-1-1−ii1-11-1-111-1−i−iiii−iii−i−i-1-111ii−i−i-11−ii−ii-11i−i
χ281-1-111-1-1111-11-1-1-11-1-11111-1-11−i−iii-1-1-111ii−i−i-1-111−ii1-1-11-11-11ii−i−ii−iii−i−i11-1-1−i−iii-11i−i−ii1-1−ii
χ291-1-111-1-1111-11-1-1-11-1-111-1-1111ii−i−i-111-1-1−i−iii11-1-1i−i-11-11-11-11ii−i−i−iiii−i−i-1-111−i−iii1-1−ii−ii1-1i−i
χ301-1-111-1-1111-11-1-1-11-1-111-1-1111ii−i−i-1-1-111−i−iii-1-111i−i-111-1-111-1−i−iii−iiii−i−i11-1-1ii−i−i1-1i−i−ii-11−ii
χ311-1-111-1-1111-11-1-1-11-1-111-1-1111−i−iii-111-1-1ii−i−i11-1-1−ii-11-11-11-11−i−iiii−i−i−iii-1-111ii−i−i1-1i−ii−i1-1−ii
χ321-1-111-1-1111-11-1-1-11-1-111-1-1111−i−iii-1-1-111ii−i−i-1-111−ii-111-1-111-1ii−i−ii−i−i−iii11-1-1−i−iii1-1−iii−i-11i−i
χ332222222222-2-2-222-222220000-22222-2000022220000-2-20000-2-2000000-2-20000000000000000000000
χ342222222222-2-2-222-222220000-2-2-2-2-2-20000-2-2-2-20000220000-2-2000000220000000000000000000000
χ352222222222-2-2-222-2-2-2-2-20000-22222-20000-2-2-2-20000-2-2000022000000220000000000000000000000
χ362222222222-2-2-222-2-2-2-2-20000-2-2-2-2-2-200002222000022000022000000-2-20000000000000000000000
χ3722222222-2-2222-2-2200002222-20000-222220000-2-2-2-200-2-22200-2-20000000000000000000000000000
χ3822222222-2-2222-2-2200002222-20000-2-2-2-2-20000222200-2-2-2-200220000000000000000000000000000
χ3922222222-2-2222-2-220000-2-2-2-2-20000-222220000-2-2-2-20022-2-200220000000000000000000000000000
χ4022222222-2-2222-2-220000-2-2-2-2-20000-2-2-2-2-20000222200222200-2-20000000000000000000000000000
χ4122-22-2-22-22-20002-202-22-2000002-22-20i2−i2i2−i22-22-2i2−i2i2−i20000000000i2−i2i2−i2000000i2−i2i2−i2i2−i2i2−i20000000000
χ4222-22-2-22-22-20002-202-22-2000002-22-20−i2i2−i2i22-22-2−i2i2−i2i20000000000−i2i2−i2i2000000−i2i2−i2i2−i2i2−i2i20000000000
χ4322-22-2-22-22-20002-202-22-200000-22-220i2−i2i2−i2-22-22i2−i2i2−i20000000000−i2i2−i2i2000000i2−i2i2−i2−i2i2−i2i20000000000
χ4422-22-2-22-22-20002-202-22-200000-22-220−i2i2−i2i2-22-22−i2i2−i2i20000000000i2−i2i2−i2000000−i2i2−i2i2i2−i2i2−i20000000000
χ4522-22-2-22-22-20002-20-22-22000002-22-20i2−i2i2−i2-22-22i2−i2i2−i20000000000i2−i2i2−i2000000−i2i2−i2i2−i2i2−i2i20000000000
χ4622-22-2-22-22-20002-20-22-22000002-22-20−i2i2−i2i2-22-22−i2i2−i2i20000000000−i2i2−i2i2000000i2−i2i2−i2i2−i2i2−i20000000000
χ4722-22-2-22-22-20002-20-22-2200000-22-220i2−i2i2−i22-22-2i2−i2i2−i20000000000−i2i2−i2i2000000−i2i2−i2i2i2−i2i2−i20000000000
χ4822-22-2-22-22-20002-20-22-2200000-22-220−i2i2−i2i22-22-2−i2i2−i2i20000000000i2−i2i2−i2000000i2−i2i2−i2−i2i2−i2i20000000000
χ492-222-22-2-22-2000-2202-2-22000002i−2i−2i2i0i2−i2−i2i22i−2i−2i2ii2−i2−i2i20000000000−222−2000000i2−i2−i2i2−222−20000000000
χ502-222-22-2-22-2000-2202-2-22000002i−2i−2i2i0−i2i2i2−i22i−2i−2i2i−i2i2i2−i200000000002−2−22000000−i2i2i2−i22−2−220000000000
χ512-222-22-2-22-2000-2202-2-2200000−2i2i2i−2i0i2−i2−i2i2−2i2i2i−2ii2−i2−i2i200000000002−2−22000000i2−i2−i2i22−2−220000000000
χ522-222-22-2-22-2000-2202-2-2200000−2i2i2i−2i0−i2i2i2−i2−2i2i2i−2i−i2i2i2−i20000000000−222−2000000−i2i2i2−i2−222−20000000000
χ532-222-22-2-22-2000-220-222-2000002i−2i−2i2i0i2−i2−i2i2−2i2i2i−2ii2−i2−i2i20000000000−222−2000000−i2i2i2−i22−2−220000000000
χ542-222-22-2-22-2000-220-222-2000002i−2i−2i2i0−i2i2i2−i2−2i2i2i−2i−i2i2i2−i200000000002−2−22000000i2−i2−i2i2−222−20000000000
χ552-222-22-2-22-2000-220-222-200000−2i2i2i−2i0i2−i2−i2i22i−2i−2i2ii2−i2−i2i200000000002−2−22000000−i2i2i2−i2−222−20000000000
χ562-222-22-2-22-2000-220-222-200000−2i2i2i−2i0−i2i2i2−i22i−2i−2i2i−i2i2i2−i20000000000−222−2000000i2−i2−i2i22−2−220000000000
χ572-2-222-2-22222-22-2-2-222-2-20000-22i2i−2i−2i200002i2i−2i−2i0000−2i2i0000-22000000−2i2i0000000000000000000000
χ582-2-222-2-22222-22-2-2-222-2-20000-2−2i−2i2i2i20000−2i−2i2i2i00002i−2i0000-220000002i−2i0000000000000000000000
χ592-2-222-2-22222-22-2-2-2-2-2220000-22i2i−2i−2i20000−2i−2i2i2i0000−2i2i00002-20000002i−2i0000000000000000000000
χ602-2-222-2-22222-22-2-2-2-2-2220000-2−2i−2i2i2i200002i2i−2i−2i00002i−2i00002-2000000−2i2i0000000000000000000000
χ612-2-222-2-22-2-2-22-2222000022-2-2-20000222-2-20000-2-22200-222-200-220000000000000000000000000000
χ622-2-222-2-22-2-2-22-2222000022-2-2-200002-2-222000022-2-200-22-22002-20000000000000000000000000000
χ632-2-222-2-22-2-2-22-22220000-2-222-20000222-2-20000-2-222002-2-22002-20000000000000000000000000000
χ642-2-222-2-22-2-2-22-22220000-2-222-200002-2-222000022-2-2002-22-200-220000000000000000000000000000
χ6544444444-4-4-4-4-4-4-4-40000000040000400000000000000000000000000000000000000000000000000
χ6644-44-4-44-4-44000-440000000000000002i2−2i22i2−2i20000−2i22i2−2i22i200000000000000000000000000000000000000
χ6744-44-4-44-4-44000-44000000000000000−2i22i2−2i22i200002i2−2i22i2−2i200000000000000000000000000000000000000
χ6844-4-4-44-440044-400-40000000000000000000000000000000000000000002i2−2i22i2−2i2000000000000000000
χ6944-4-4-44-440044-400-4000000000000000000000000000000000000000000−2i22i2−2i22i2000000000000000000
χ7044-4-4-44-4400-4-4400400004-44-400000000000000000000000000000000000000000000000000000000
χ7144-4-4-44-4400-4-440040000-44-4400000000000000000000000000000000000000000000000000000000
χ724-444-44-4-4-440004-40000000000000002i2−2i2−2i22i20000−2i22i22i2−2i200000000000000000000000000000000000000
χ734-444-44-4-4-440004-4000000000000000−2i22i22i2−2i200002i2−2i2−2i22i200000000000000000000000000000000000000
χ744-44-4-4-444004-4-400400004-4-4400000000000000000000000000000000000000000000000000000000
χ754-44-4-4-444004-4-40040000-444-400000000000000000000000000000000000000000000000000000000
χ764-44-4-4-44400-44400-400000000000000000000000000000000000000000022−22−2222000000000000000000
χ774-44-4-4-44400-44400-4000000000000000000000000000000000000000000−222222−22000000000000000000
χ784-4-444-4-44-4-44-4444-40000000040000-400000000000000000000000000000000000000000000000000
χ79888-88-8-8-8000000000000000000000000000000000000000000000000000000000000000000000000
χ808-8-8-8888-8000000000000000000000000000000000000000000000000000000000000000000000000

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