Finite Group Databasebeta

← Group #229363

Character table — Group #229363

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222244444444444444444444444444888888888888888888888888888816161616161616161616
order12222222444444444444444444444488888888888844444444448888888888888888882244444488
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-1-1-1
χ31111111111111111111111111-1-1-1-11111111111111-1-1-1-111-1-111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-11111
χ5111111111111111111111-1-1-1-111111-1-1-1-1111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1-11111-1-111
χ7111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ8111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-11111-1-1111111-1-1-1-111-1-1
χ911111111111111111-1-1-1-1111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1
χ1011111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-11111
χ1111111111111111111-1-1-1-11111-1-1-1-11-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111
χ1211111111111111111-1-1-1-11111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111111111-1-1-1-1-1-11111-1-11111-1-1-1-1
χ1311111111111111111-1-1-1-1-1-1-1-1111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111
χ1411111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-111-1-111-1-1
χ1511111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1
χ1611111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111111111-1-1-1-111-1-111-1-111
χ1711-11-1-11-1-11-1-1-11111ii−i−iii−i−iii−i−i-111-1-1iiii−i−i−i−ii−i1-1i−i1-1i−iii−i−i11-1-111-1-11-1ii−i−i1-1i−i1-1i−i1-1
χ1811-11-1-11-1-11-1-1-11111ii−i−iii−i−iii−i−i-111-1-1−i−i−i−iiiiii−i-11i−i-11i−iii−i−i-1-111-1-1111-1−i−iii1-1−ii1-1−ii-11
χ1911-11-1-11-1-11-1-1-11111ii−i−iii−i−i−i−iii-111-1-1iiii−i−i−i−i−ii-11i−i-11i−i−i−iii11-1-111-1-11-1ii−i−i-11−ii-11−ii-11
χ2011-11-1-11-1-11-1-1-11111ii−i−iii−i−i−i−iii-111-1-1−i−i−i−iiiii−ii1-1i−i1-1i−i−i−iii-1-111-1-1111-1−i−iii-11i−i-11i−i1-1
χ2111-11-1-11-1-11-1-1-11111ii−i−i−i−iiiii−i−i-1-1-111iiii−i−i−i−ii−i1-1−ii1-1i−i−i−iii11-1-1-1-111-11−i−iii-11−ii1-1i−i-11
χ2211-11-1-11-1-11-1-1-11111ii−i−i−i−iiiii−i−i-1-1-111−i−i−i−iiiiii−i-11−ii-11i−i−i−iii-1-11111-1-1-11ii−i−i-11i−i1-1−ii1-1
χ2311-11-1-11-1-11-1-1-11111ii−i−i−i−iii−i−iii-1-1-111iiii−i−i−i−i−ii-11−ii-11i−iii−i−i11-1-1-1-111-11−i−iii1-1i−i-11−ii1-1
χ2411-11-1-11-1-11-1-1-11111ii−i−i−i−iii−i−iii-1-1-111−i−i−i−iiiii−ii1-1−ii1-1i−iii−i−i-1-11111-1-1-11ii−i−i1-1−ii-11i−i-11
χ2511-11-1-11-1-11-1-1-11111−i−iiiii−i−iii−i−i-1-1-111iiii−i−i−i−ii−i1-1i−i1-1−ii−i−iii-1-11111-1-1-11−i−iii1-1i−i-11−ii-11
χ2611-11-1-11-1-11-1-1-11111−i−iiiii−i−iii−i−i-1-1-111−i−i−i−iiiiii−i-11i−i-11−ii−i−iii11-1-1-1-111-11ii−i−i1-1−ii-11i−i1-1
χ2711-11-1-11-1-11-1-1-11111−i−iiiii−i−i−i−iii-1-1-111iiii−i−i−i−i−ii-11i−i-11−iiii−i−i-1-11111-1-1-11−i−iii-11−ii1-1i−i1-1
χ2811-11-1-11-1-11-1-1-11111−i−iiiii−i−i−i−iii-1-1-111−i−i−i−iiiii−ii1-1i−i1-1−iiii−i−i11-1-1-1-111-11ii−i−i-11i−i1-1−ii-11
χ2911-11-1-11-1-11-1-1-11111−i−iii−i−iiiii−i−i-111-1-1iiii−i−i−i−ii−i1-1−ii1-1−iiii−i−i-1-111-1-1111-1ii−i−i-11−ii-11−ii1-1
χ3011-11-1-11-1-11-1-1-11111−i−iii−i−iiiii−i−i-111-1-1−i−i−i−iiiiii−i-11−ii-11−iiii−i−i11-1-111-1-11-1−i−iii-11i−i-11i−i-11
χ3111-11-1-11-1-11-1-1-11111−i−iii−i−iii−i−iii-111-1-1iiii−i−i−i−i−ii-11−ii-11−ii−i−iii-1-111-1-1111-1ii−i−i1-1i−i1-1i−i-11
χ3211-11-1-11-1-11-1-1-11111−i−iii−i−iii−i−iii-111-1-1−i−i−i−iiiii−ii1-1−ii1-1−ii−i−iii11-1-111-1-11-1−i−iii1-1−ii1-1−ii1-1
χ332222222222-2-22-2-22-2222222220000-22222000000000000-2-200-2-2000000000000-2-200000000000000
χ342222222222-2-22-2-22-22222-2-2-2-20000-2-2-2-2-20000000000002200-2-20000000000002200000000000000
χ352222222222-2-22-2-22-2-2-2-2-222220000-2-2-2-2-2000000000000-2-200220000000000002200000000000000
χ362222222222-2-22-2-22-2-2-2-2-2-2-2-2-20000-22222000000000000220022000000000000-2-200000000000000
χ3722222222-2-222-222-2-2000000002222-2000022-2-222-2-2-2-22200-2-2000000000000000000000000000000
χ3822222222-2-222-222-2-2000000002222-20000-2-222-2-222-2-2-2-20022000000000000000000000000000000
χ3922222222-2-222-222-2-200000000-2-2-2-2-2000022-2-222-2-222-2-20022000000000000000000000000000000
χ4022222222-2-222-222-2-200000000-2-2-2-2-20000-2-222-2-222222200-2-2000000000000000000000000000000
χ41222-2-2-2-222-200-200202i−2i2i−2i2-22-2000002i−2i2i−2ii2−i2i2−i2i2−i2i2−i2000000000000002−22−2i2−i2i2−i2002−22−20000000000
χ42222-2-2-2-222-200-200202i−2i2i−2i2-22-2000002i−2i2i−2i−i2i2−i2i2−i2i2−i2i200000000000000−22−22−i2i2−i2i200−22−220000000000
χ43222-2-2-2-222-200-200202i−2i2i−2i-22-2200000−2i2i−2i2ii2−i2i2−i2i2−i2i2−i2000000000000002−22−2−i2i2−i2i200−22−220000000000
χ44222-2-2-2-222-200-200202i−2i2i−2i-22-2200000−2i2i−2i2i−i2i2−i2i2−i2i2−i2i200000000000000−22−22i2−i2i2−i2002−22−20000000000
χ45222-2-2-2-222-200-20020−2i2i−2i2i2-22-200000−2i2i−2i2ii2−i2i2−i2i2−i2i2−i200000000000000−22−22i2−i2i2−i200−22−220000000000
χ46222-2-2-2-222-200-20020−2i2i−2i2i2-22-200000−2i2i−2i2i−i2i2−i2i2−i2i2−i2i2000000000000002−22−2−i2i2−i2i2002−22−20000000000
χ47222-2-2-2-222-200-20020−2i2i−2i2i-22-22000002i−2i2i−2ii2−i2i2−i2i2−i2i2−i200000000000000−22−22−i2i2−i2i2002−22−20000000000
χ48222-2-2-2-222-200-20020−2i2i−2i2i-22-22000002i−2i2i−2i−i2i2−i2i2−i2i2−i2i2000000000000002−22−2i2−i2i2−i200−22−220000000000
χ4922-22-2-22-22-2-2-2222-2-2000000002i2i−2i−2i200002i2i−2i−2i−2i−2i2i2i−2i2i2-200-22000000000000000000000000000000
χ5022-22-2-22-22-2-2-2222-2-2000000002i2i−2i−2i20000−2i−2i2i2i2i2i−2i−2i−2i2i-22002-2000000000000000000000000000000
χ5122-22-2-22-22-2-2-2222-2-200000000−2i−2i2i2i200002i2i−2i−2i−2i−2i2i2i2i−2i-22002-2000000000000000000000000000000
χ5222-22-2-22-22-2-2-2222-2-200000000−2i−2i2i2i20000−2i−2i2i2i2i2i−2i−2i2i−2i2-200-22000000000000000000000000000000
χ5322-22-2-22-2-2222-2-2-22-22i2i−2i−2i2i2i−2i−2i0000222-2-2000000000000−2i2i00−2i2i000000000000-2200000000000000
χ5422-22-2-22-2-2222-2-2-22-22i2i−2i−2i−2i−2i2i2i00002-2-2220000000000002i−2i00−2i2i0000000000002-200000000000000
χ5522-22-2-22-2-2222-2-2-22-2−2i−2i2i2i2i2i−2i−2i00002-2-222000000000000−2i2i002i−2i0000000000002-200000000000000
χ5622-22-2-22-2-2222-2-2-22-2−2i−2i2i2i−2i−2i2i2i0000222-2-20000000000002i−2i002i−2i000000000000-2200000000000000
χ5722-2-222-2-2-2-200200202-2-222i−2i−2i2i00000−2i2i2i−2i2−22−2−22−22000000000000002−2−22−i2i2i2−i200i2−i2−i2i20000000000
χ5822-2-222-2-2-2-200200202-2-222i−2i−2i2i00000−2i2i2i−2i−22−222−22−200000000000000−222−2i2−i2−i2i200−i2i2i2−i20000000000
χ5922-2-222-2-2-2-200200202-2-22−2i2i2i−2i000002i−2i−2i2i2−22−2−22−22000000000000002−2−22i2−i2−i2i200−i2i2i2−i20000000000
χ6022-2-222-2-2-2-200200202-2-22−2i2i2i−2i000002i−2i−2i2i−22−222−22−200000000000000−222−2−i2i2i2−i200i2−i2−i2i20000000000
χ6122-2-222-2-2-2-20020020-222-22i−2i−2i2i000002i−2i−2i2i2−22−2−22−2200000000000000−222−2−i2i2i2−i200−i2i2i2−i20000000000
χ6222-2-222-2-2-2-20020020-222-22i−2i−2i2i000002i−2i−2i2i−22−222−22−2000000000000002−2−22i2−i2−i2i200i2−i2−i2i20000000000
χ6322-2-222-2-2-2-20020020-222-2−2i2i2i−2i00000−2i2i2i−2i2−22−2−22−2200000000000000−222−2i2−i2−i2i200i2−i2−i2i20000000000
χ6422-2-222-2-2-2-20020020-222-2−2i2i2i−2i00000−2i2i2i−2i−22−222−22−2000000000000002−2−22−i2i2i2−i200−i2i2i2−i20000000000
χ6544444444-4-4-4-4-4-4-4-44000000000000400000000000000000000000000000000000000000000000000
χ66444-4-4-4-44-4400400-40000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000000
χ67444-4-4-4-44-4400400-4000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000000
χ6844-44-4-44-44-4444-4-4-44000000000000-400000000000000000000000000000000000000000000000000
χ6944-4-444-4-44400-400-400000000000000000022−22−2222−222222−2200000000000000000000000000000000000000
χ7044-4-444-4-44400-400-4000000000000000000−222222−2222−22−222200000000000000000000000000000000000000
χ714-44-44-44-4004-404-400000000000000000000000000000000000002i2−2i22i2−2i2000000000000000000000000
χ724-44-44-44-4004-404-40000000000000000000000000000000000000−2i22i2−2i22i2000000000000000000000000
χ734-44-44-44-400-440-4400000000004i−4i4i−4i000000000000000000000000000000000000000000000000000
χ744-44-44-44-400-440-440000000000−4i4i−4i4i000000000000000000000000000000000000000000000000000
χ754-4-4-4-4444004-40-4400000000004-4-44000000000000000000000000000000000000000000000000000
χ764-4-4-4-4444004-40-440000000000-444-4000000000000000000000000000000000000000000000000000
χ774-4-4-4-444400-4404-4000000000000000000000000000000000000022−22−2222000000000000000000000000
χ784-4-4-4-444400-4404-40000000000000000000000000000000000000−222222−22000000000000000000000000
χ798-888-88-8-8000000000000000000000000000000000000000000000000000000000000000000000000
χ808-8-888-8-88000000000000000000000000000000000000000000000000000000000000000000000000

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