Finite Group Databasebeta

← Group #269790

Character table — Group #269790

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888882244444488888888888888882244444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1111111-1-1-1-111-1-1-1111-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111-1-1111111111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111
χ5111111111111111111111-1-1-1-111111111111-1-111-1-111111111-1-1-1-11111-1-1-1-1-11-1-111-1-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111
χ7111111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-111-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1111
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1111-11111-1-1-1
χ911111111111111111-1-1-1-11111111111111-1-111-1-11111-1-1-1-11111111111-1-11-1-1-1-1-1-1-111-1
χ1011111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-1-111-1-1-111-1-11
χ1111111111111111111-1-1-1-111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111111-1-11
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-111111-1-111-1
χ1311111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1111111-111-111-1-1-1-11
χ1411111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111-1-1-1111111-1
χ1511111111111111111-1-1-1-1-1-1-1-11-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1111-1-11111-1
χ1611111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111111111111-1-11-1-1-1-1-1-11
χ172222222222-22-2-2-22-222220000-2222200002200-2-200000000-2-20000000000000-20000000
χ182222222222-22-2-2-22-222220000-2-2-2-2-20000-2-200-2-20000000022000000000000020000000
χ192222222222-22-2-2-22-2-2-2-2-20000-222220000-2-2002200000000-2-2000000000000020000000
χ202222222222-22-2-2-22-2-2-2-2-20000-2-2-2-2-2000022002200000000220000000000000-20000000
χ2122222222-2-22-2222-2-200002222-200002222002200-2-2-2-20000000000000000-20000000000
χ2222222222-2-22-2222-2-200002222-20000-2-2-2-200-2-200-2-222000000000000000020000000000
χ2322222222-2-22-2222-2-20000-2-2-2-2-20000222200-2-20022-2-2000000000000000020000000000
χ2422222222-2-22-2222-2-20000-2-2-2-2-20000-2-2-2-200220022220000000000000000-20000000000
χ2522-2-222-2-22-20-2000202i2i−2i−2i000002i2i−2i−2i22−2−22-20000002−2i2i2−i2−i2000000i2i2−i2−i2000000002−2000
χ2622-2-222-2-22-20-2000202i2i−2i−2i000002i2i−2i−2i−2−2222-2000000−22−i2−i2i2i2000000−i2−i2i2i200000000−22000
χ2722-2-222-2-22-20-2000202i2i−2i−2i00000−2i−2i2i2i22−2−2-220000002−2i2i2−i2−i2000000−i2−i2i2i200000000−22000
χ2822-2-222-2-22-20-2000202i2i−2i−2i00000−2i−2i2i2i−2−222-22000000−22−i2−i2i2i2000000i2i2−i2−i2000000002−2000
χ2922-2-222-2-22-20-200020−2i−2i2i2i000002i2i−2i−2i22−2−2-220000002−2−i2−i2i2i2000000i2i2−i2−i200000000−22000
χ3022-2-222-2-22-20-200020−2i−2i2i2i000002i2i−2i−2i−2−222-22000000−22i2i2−i2−i2000000−i2−i2i2i2000000002−2000
χ3122-2-222-2-22-20-200020−2i−2i2i2i00000−2i−2i2i2i22−2−22-20000002−2−i2−i2i2i2000000−i2−i2i2i2000000002−2000
χ3222-2-222-2-22-20-200020−2i−2i2i2i00000−2i−2i2i2i−2−2222-2000000−22i2i2−i2−i2000000i2i2−i2−i200000000−22000
χ332-22-2-222-200-2022-20000002i2i−2i−2i0i2−i2i2−i22-22-2002i−2i0000000000i2−i222−2−2i2−i2i2−i200000000002−20
χ342-22-2-222-200-2022-20000002i2i−2i−2i0i2−i2i2−i2-22-2200−2i2i0000000000i2−i222−2−2−i2i2−i2i20000000000−220
χ352-22-2-222-200-2022-20000002i2i−2i−2i0−i2i2−i2i22-22-2002i−2i0000000000−i2i2−2−222−i2i2−i2i20000000000−220
χ362-22-2-222-200-2022-20000002i2i−2i−2i0−i2i2−i2i2-22-2200−2i2i0000000000−i2i2−2−222i2−i2i2−i200000000002−20
χ372-22-2-222-200-2022-2000000−2i−2i2i2i0i2−i2i2−i22-22-200−2i2i0000000000i2−i2−2−222i2−i2i2−i20000000000−220
χ382-22-2-222-200-2022-2000000−2i−2i2i2i0i2−i2i2−i2-22-22002i−2i0000000000i2−i2−2−222−i2i2−i2i200000000002−20
χ392-22-2-222-200-2022-2000000−2i−2i2i2i0−i2i2−i2i22-22-200−2i2i0000000000−i2i222−2−2−i2i2−i2i200000000002−20
χ402-22-2-222-200-2022-2000000−2i−2i2i2i0−i2i2−i2i2-22-22002i−2i0000000000−i2i222−2−2i2−i2i2−i20000000000−220
χ412-2-2-22-222222-2-22-2-2200002-22-2-2000000000000002-2002i−2i2i−2i00000000000002i−2i00000000
χ422-2-2-22-222222-2-22-2-2200002-22-2-2000000000000002-200−2i2i−2i2i0000000000000−2i2i00000000
χ432-2-2-22-222222-2-22-2-220000-22-22-200000000000000-22002i−2i2i−2i0000000000000−2i2i00000000
χ442-2-2-22-222222-2-22-2-220000-22-22-200000000000000-2200−2i2i−2i2i00000000000002i−2i00000000
χ452-2-2-22-222-2-222-22-22-22-22-22-22-220000000000002-2-2200000000000000002-200000000000
χ462-2-2-22-222-2-222-22-22-22-22-2-22-2220000000000002-22-20000000000000000-2200000000000
χ472-2-2-22-222-2-222-22-22-2-22-222-22-22000000000000-22-220000000000000000-2200000000000
χ482-2-2-22-222-2-222-22-22-2-22-22-22-222000000000000-222-200000000000000002-200000000000
χ492-2-2-22-222-2-2-222-22222-22-20000-2000000000000-2200000000002-22-200000000002-200000
χ502-2-2-22-222-2-2-222-22222-22-20000-2000000000000-220000000000-22-220000000000-2200000
χ512-2-2-22-222-2-2-222-2222-22-220000-20000000000002-200000000002-22-20000000000-2200000
χ522-2-2-22-222-2-2-222-2222-22-220000-20000000000002-20000000000-22-2200000000002-200000
χ5344444444-4-4-4-4-4-4-4-44000000004000000000000000000000000000000000000000000000
χ5444-44-4-44-400404-4-40000000000000000000000000000000000022−22−222200000000000000000
χ5544-44-4-44-400404-4-400000000000000000000000000000000000−222222−2200000000000000000
χ5644-44-4-44-400-40-4440000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ5744-44-4-44-400-40-444000000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ5844-4-444-4-4-4404000-4000000000000002222−22−2200000000−2222000000000000000000000000000
χ5944-4-444-4-4-4404000-400000000000000−22−2222220000000022−22000000000000000000000000000
χ604-4444-4-4-44-404000-4000000000000000000000000000022−22−222200000000000000000000000
χ614-4444-4-4-44-404000-40000000000000000000000000000−222222−2200000000000000000000000
χ624-4444-4-4-4-440-4000404i−4i−4i4i00000000000000000000000000000000000000000000000000
χ634-4444-4-4-4-440-400040−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ644-44-4-444-40040-4-44000000000002i2−2i22i2−2i2000000000000000000−2i22i2000000000000000000000
χ654-44-4-444-40040-4-4400000000000−2i22i2−2i22i20000000000000000002i2−2i2000000000000000000000
χ664-4-44-44-4400000000000000000022−22−222222−22−2222000000000000000000002-2-220000000000000
χ674-4-44-44-4400000000000000000022−22−2222−222222−2200000000000000000000-222-20000000000000
χ684-4-44-44-44000000000000000000−222222−2222−22−222200000000000000000000-222-20000000000000
χ694-4-44-44-44000000000000000000−222222−22−222222−22000000000000000000002-2-220000000000000
χ704-4-4-44-44444-4-44-44-4-4000000004000000000000000000000000000000000000000000000
χ71888-8-8-8-88000000000000000000000000000000000000000000000000000000000000000

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