Finite Group Databasebeta

← Group #288079

Character table — Group #288079

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11111111222222222222222244444444444444444444444444888888888888888888161616161616161616163232
order12222222444444448888888844444488888888888888888888224444444488888888444444888824
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1111111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-11111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-11-1-11-1-11111-1-1
χ6111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-111
χ7111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111111-1-11-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-11111-111-1111111-1-1
χ91111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1111-1-111-1-11-1
χ101111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11-1-1-111-1-111-11
χ111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-11111-1111-1-1-1-111-11
χ121111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111111-1-1-11111-1-11-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-111111-1-1-11
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111111-1-1-1-1-1111-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1111111-1-1-1-1-1-1-1111-1-1111-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1111-1-1-111-1-1-11
χ172222222222-22-2-2-22000000002222-2-200002222-2-2-2-200000000-2-200-2-2002200000000000000000000
χ182222222222-22-2-2-22000000002222-2-20000-2-2-2-22222000000002200-2-200-2-200000000000000000000
χ192222222222-22-2-2-2200000000-2-2-2-2-2-200002222-2-2-2-20000000022002200-2-200000000000000000000
χ202222222222-22-2-2-2200000000-2-2-2-2-2-20000-2-2-2-2222200000000-2-20022002200000000000000000000
χ2122222222-2-22-2222-2222222220000-2-2-2-2-2-20000000000000000002200220000000000-200-200000000
χ2222222222-2-22-2222-2222222220000-2-2-2-2-2-2000000000000000000-2-200-2-20000000000200200000000
χ2322222222-2-22-2222-2-2-2-2-2-2-2-2-20000-2-222220000000000000000002200-2-20000000000200-200000000
χ2422222222-2-22-2222-2-2-2-2-2-2-2-2-20000-2-22222000000000000000000-2-200220000000000-200200000000
χ25222-22-2-2-22-20-200022222−2−2−2−222-2-20022−2−22i2i−2i−2i0000i2i2i2i2−i2−i2−i2−i2000000002i−2i22−2−2i2i2−i2−i2000000000000
χ26222-22-2-2-22-20-200022222−2−2−2−222-2-20022−2−2−2i−2i2i2i0000−i2−i2−i2−i2i2i2i2i200000000−2i2i22−2−2−i2−i2i2i2000000000000
χ27222-22-2-2-22-20-200022222−2−2−2−2-2-2220022−2−22i2i−2i−2i0000i2i2i2i2−i2−i2−i2−i200000000−2i2i−2−222−i2−i2i2i2000000000000
χ28222-22-2-2-22-20-200022222−2−2−2−2-2-2220022−2−2−2i−2i2i2i0000−i2−i2−i2−i2i2i2i2i2000000002i−2i−2−222i2i2−i2−i2000000000000
χ29222-22-2-2-22-20-20002−2−2−2−2222222-2-200−2−2222i2i−2i−2i0000−i2−i2−i2−i2i2i2i2i2000000002i−2i−2−222−i2−i2i2i2000000000000
χ30222-22-2-2-22-20-20002−2−2−2−2222222-2-200−2−222−2i−2i2i2i0000i2i2i2i2−i2−i2−i2−i200000000−2i2i−2−222i2i2−i2−i2000000000000
χ31222-22-2-2-22-20-20002−2−2−2−22222-2-22200−2−2222i2i−2i−2i0000−i2−i2−i2−i2i2i2i2i200000000−2i2i22−2−2i2i2−i2−i2000000000000
χ32222-22-2-2-22-20-20002−2−2−2−22222-2-22200−2−222−2i−2i2i2i0000i2i2i2i2−i2−i2−i2−i2000000002i−2i22−2−2−i2−i2i2i2000000000000
χ3322-22-2-2-2200-2022-202i2i−2i−2i2i2i−2i−2i0000000000i2−i2i2−i2i2i2−i2−i222−2−222−2−2002-2002i−2i0000000000000000i2−i22−200
χ3422-22-2-2-2200-2022-202i2i−2i−2i2i2i−2i−2i0000000000i2−i2i2−i2i2i2−i2−i222−2−222−2−200-2200−2i2i0000000000000000−i2i2−2200
χ3522-22-2-2-2200-2022-202i2i−2i−2i2i2i−2i−2i0000000000−i2i2−i2i2−i2−i2i2i2−2−222−2−222002-2002i−2i0000000000000000−i2i2−2200
χ3622-22-2-2-2200-2022-202i2i−2i−2i2i2i−2i−2i0000000000−i2i2−i2i2−i2−i2i2i2−2−222−2−22200-2200−2i2i0000000000000000i2−i22−200
χ3722-22-2-2-2200-2022-20−2i−2i2i2i−2i−2i2i2i0000000000i2−i2i2−i2i2i2−i2−i2−2−222−2−222002-200−2i2i0000000000000000i2−i2−2200
χ3822-22-2-2-2200-2022-20−2i−2i2i2i−2i−2i2i2i0000000000i2−i2i2−i2i2i2−i2−i2−2−222−2−22200-22002i−2i0000000000000000−i2i22−200
χ3922-22-2-2-2200-2022-20−2i−2i2i2i−2i−2i2i2i0000000000−i2i2−i2i2−i2−i2i2i222−2−222−2−2002-200−2i2i0000000000000000−i2i22−200
χ4022-22-2-2-2200-2022-20−2i−2i2i2i−2i−2i2i2i0000000000−i2i2−i2i2−i2−i2i2i222−2−222−2−200-22002i−2i0000000000000000i2−i2−2200
χ412-2-222-22-22-202000-22−22−22−22−22i−2i2i−2i002−22−200002i−2i2i−2ii2−i2i2−i2i2−i2i2−i22-200000000i2−i2i2−i22−22−2000000000000
χ422-2-222-22-22-202000-22−22−22−22−22i−2i2i−2i002−22−20000−2i2i−2i2i−i2i2−i2i2−i2i2−i2i2-2200000000i2−i2i2−i2−22−22000000000000
χ432-2-222-22-22-202000-22−22−22−22−2−2i2i−2i2i002−22−200002i−2i2i−2ii2−i2i2−i2i2−i2i2−i2-2200000000−i2i2−i2i2−22−22000000000000
χ442-2-222-22-22-202000-22−22−22−22−2−2i2i−2i2i002−22−20000−2i2i−2i2i−i2i2−i2i2−i2i2−i2i22-200000000−i2i2−i2i22−22−2000000000000
χ452-2-222-22-22-202000-2−22−22−22−222i−2i2i−2i00−22−2200002i−2i2i−2i−i2i2−i2i2−i2i2−i2i22-200000000−i2i2−i2i2−22−22000000000000
χ462-2-222-22-22-202000-2−22−22−22−222i−2i2i−2i00−22−220000−2i2i−2i2ii2−i2i2−i2i2−i2i2−i2-2200000000−i2i2−i2i22−22−2000000000000
χ472-2-222-22-22-202000-2−22−22−22−22−2i2i−2i2i00−22−2200002i−2i2i−2i−i2i2−i2i2−i2i2−i2i2-2200000000i2−i2i2−i22−22−2000000000000
χ482-2-222-22-22-202000-2−22−22−22−22−2i2i−2i2i00−22−220000−2i2i−2i2ii2−i2i2−i2i2−i2i2−i22-200000000i2−i2i2−i2−22−22000000000000
χ492-2-2-222-22222-2-22-2-2000000002i−2i−2i2i-220000000000002-22-2-22-2200002i−2i00000000−2i2i2i−2i000000000000
χ502-2-2-222-22222-2-22-2-2000000002i−2i−2i2i-22000000000000-22-222-22-200002i−2i000000002i−2i−2i2i000000000000
χ512-2-2-222-22222-2-22-2-200000000−2i2i2i−2i-220000000000002-22-2-22-220000−2i2i000000002i−2i−2i2i000000000000
χ522-2-2-222-22222-2-22-2-200000000−2i2i2i−2i-22000000000000-22-222-22-20000−2i2i00000000−2i2i2i−2i000000000000
χ532-2-2-222-2222-2-22-22-22-22-2-22-222i−2i−2i2i2-22-2-2200000000000000000000−2i2i00002i−2i−2i2i0000000000000000
χ542-2-2-222-2222-2-22-22-22-22-2-22-22−2i2i2i−2i2-22-2-22000000000000000000002i−2i0000−2i2i2i−2i0000000000000000
χ552-2-2-222-2222-2-22-22-2-22-222-22-22i−2i−2i2i2-2-222-200000000000000000000−2i2i0000−2i2i2i−2i0000000000000000
χ562-2-2-222-2222-2-22-22-2-22-222-22-2−2i2i2i−2i2-2-222-2000000000000000000002i−2i00002i−2i−2i2i0000000000000000
χ572-2-2-222-22-2-2-222-2222-22-2-22-220000-22-222-2000000000000000000000000000000000002-202-2000000
χ582-2-2-222-22-2-2-222-2222-22-2-22-220000-22-222-200000000000000000000000000000000000-220-22000000
χ592-2-2-222-22-2-2-222-222-22-222-22-20000-222-2-22000000000000000000000000000000000002-20-22000000
χ602-2-2-222-22-2-2-222-222-22-222-22-20000-222-2-2200000000000000000000000000000000000-2202-2000000
χ6144444444-4-4-4-4-4-4-4-40000000000004400000000000000000000000000000000000000000000000000
χ62444-44-4-4-4-4404000-422222222−22−22−22−22000000−22−2222220000000000000000000000000000000000000000000000
χ63444-44-4-4-4-4404000-4−22−22−22−22222222220000002222−22−220000000000000000000000000000000000000000000000
χ6444-44-4-4-440040-4-4400000000000000000002i2−2i22i2−2i2−2i2−2i22i22i200000000000000000000000000000000000000
χ6544-44-4-4-440040-4-440000000000000000000−2i22i2−2i22i22i22i2−2i2−2i200000000000000000000000000000000000000
χ6644-4-4-444-4000000002i22i2−2i2−2i2−2i2−2i22i22i2000000000022−22−22220000−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000
χ6744-4-4-444-4000000002i22i2−2i2−2i2−2i2−2i22i22i20000000000−222222−2200002i2i−2i−2i−2i−2i2i2i000000000000000000000000000000
χ6844-4-4-444-400000000−2i2−2i22i22i22i22i2−2i2−2i2000000000022−22−222200002i2i−2i−2i−2i−2i2i2i000000000000000000000000000000
χ6944-4-4-444-400000000−2i2−2i22i22i22i22i2−2i2−2i20000000000−222222−220000−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000
χ704-444-44-4-4000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000022−22−2222−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000
χ714-444-44-4-4000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000−222222−222i−2i−2i2i2i−2i−2i2i000000000000000000000000000000
χ724-444-44-4-400000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000022−22−22222i−2i−2i2i2i−2i−2i2i000000000000000000000000000000
χ734-444-44-4-400000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000−222222−22−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000
χ744-44-4-4-44400404-4-404i−4i−4i4i−4i4i4i−4i00000000000000000000000000000000000000000000000000000000
χ754-44-4-4-44400404-4-40−4i4i4i−4i4i−4i−4i4i00000000000000000000000000000000000000000000000000000000
χ764-44-4-4-44400-40-44400000000000000000000000000022−22−2222−222222−22000000000000000000000000000000
χ774-44-4-4-44400-40-444000000000000000000000000000−222222−2222−22−2222000000000000000000000000000000
χ784-4-444-44-4-440-4000422−2222−2222−2222−22000000−2222−22220000000000000000000000000000000000000000000000
χ794-4-444-44-4-440-40004−2222−2222−2222−222200000022−2222−220000000000000000000000000000000000000000000000
χ804-4-4-444-44-4-444-44-440000000000004-400000000000000000000000000000000000000000000000000

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