Finite Group Databasebeta

← Group #309531

Character table — Group #309531

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888882244444488888888888888884444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1111-111-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111-1-1111111-1-1111111-1-1-1-1-1-1-1-11111-11-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111
χ5111111111111111111111-1-1-1-1111111111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-11-1-1-1-111-1
χ6111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-111-1-1-1-1-1-111-1-11
χ7111111111111111111111-1-1-1-11-1-1-1-1111111-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-11-111-1-111-1
χ911111111111111111-1-1-1-111111111111111111-1-1-1-111111111-1-1-1-11111-1-1-1-11-1-1-111-1-1-1
χ1011111111111111111-1-1-1-1111111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1111
χ1111111111111111111-1-1-1-111111-1-1-1-11111-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1111
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111111-1-1-111111-1-1-1
χ1311111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11
χ1411111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-111-11111111-1
χ1511111111111111111-1-1-1-1-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111-1-1-11111-1
χ1611111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1111111111111-1-11111-1-1-1-1-1-11
χ1722222222222-2-2-2-22-200002222-22222000022-2-20000-2-2000000000000000000-200000000
χ1822222222222-2-2-2-22-200002222-2-2-2-2-20000-2-2-2-2000022000000000000000000200000000
χ1922222222222-2-2-2-22-20000-2-2-2-2-222220000-2-2220000-2-2000000000000000000200000000
χ2022222222222-2-2-2-22-20000-2-2-2-2-2-2-2-2-200002222000022000000000000000000-200000000
χ2122222222-2-2-22222-2-222220000-200002222000022-2-200-2-200000000000000000-20000000
χ2222222222-2-2-22222-2-222220000-20000-2-2-2-20000-2-2-2-200220000000000000000020000000
χ2322222222-2-2-22222-2-2-2-2-2-20000-2000022220000-2-22200-2-20000000000000000020000000
χ2422222222-2-2-22222-2-2-2-2-2-20000-20000-2-2-2-200002222002200000000000000000-20000000
χ2522-222-2-2-2-22-200002000002i2i−2i−2i02i2i−2i−2i22−2−22-2000000002−2i2i2−i2−i20000i2i2−i2−i2000000002−2000
χ2622-222-2-2-2-22-200002000002i2i−2i−2i02i2i−2i−2i−2−2222-200000000−22−i2−i2i2i20000−i2−i2i2i200000000−22000
χ2722-222-2-2-2-22-200002000002i2i−2i−2i0−2i−2i2i2i22−2−2-22000000002−2i2i2−i2−i20000−i2−i2i2i200000000−22000
χ2822-222-2-2-2-22-200002000002i2i−2i−2i0−2i−2i2i2i−2−222-2200000000−22−i2−i2i2i20000i2i2−i2−i2000000002−2000
χ2922-222-2-2-2-22-20000200000−2i−2i2i2i02i2i−2i−2i22−2−2-22000000002−2−i2−i2i2i20000i2i2−i2−i200000000−22000
χ3022-222-2-2-2-22-20000200000−2i−2i2i2i02i2i−2i−2i−2−222-2200000000−22i2i2−i2−i20000−i2−i2i2i2000000002−2000
χ3122-222-2-2-2-22-20000200000−2i−2i2i2i0−2i−2i2i2i22−2−22-2000000002−2−i2−i2i2i20000−i2−i2i2i2000000002−2000
χ3222-222-2-2-2-22-20000200000−2i−2i2i2i0−2i−2i2i2i−2−2222-200000000−22i2i2−i2−i20000i2i2−i2−i200000000−22000
χ332-22-222-2-22-2-222-2-22-200002i−2i2i−2i200000000002i−2i00000000000022-2-200000000002i−2i00000
χ342-22-222-2-22-2-222-2-22-200002i−2i2i−2i200000000002i−2i000000000000-2-2220000000000−2i2i00000
χ352-22-222-2-22-2-222-2-22-20000−2i2i−2i2i20000000000−2i2i00000000000022-2-20000000000−2i2i00000
χ362-22-222-2-22-2-222-2-22-20000−2i2i−2i2i20000000000−2i2i000000000000-2-22200000000002i−2i00000
χ372-22-222-2-22-2-2-2-222222i2i−2i−2i2i−2i2i−2i-20000000000−2i2i002i−2i0000000000000000002-2000000000
χ382-22-222-2-22-2-2-2-222222i2i−2i−2i−2i2i−2i2i-200000000002i−2i002i−2i000000000000000000-22000000000
χ392-22-222-2-22-2-2-2-22222−2i−2i2i2i2i−2i2i−2i-20000000000−2i2i00−2i2i000000000000000000-22000000000
χ402-22-222-2-22-2-2-2-22222−2i−2i2i2i−2i2i−2i2i-200000000002i−2i00−2i2i0000000000000000002-2000000000
χ412-22-222-2-2-222-2-222-2-22i2i−2i−2i0000200000000000000−2i2i00002-22-2000000002i−2i00000000000
χ422-22-222-2-2-222-2-222-2-22i2i−2i−2i0000200000000000000−2i2i0000-22-2200000000−2i2i00000000000
χ432-22-222-2-2-222-2-222-2-2−2i−2i2i2i00002000000000000002i−2i00002-22-200000000−2i2i00000000000
χ442-22-222-2-2-222-2-222-2-2−2i−2i2i2i00002000000000000002i−2i0000-22-22000000002i−2i00000000000
χ452-2-22-222-20002-22-2002-22-200000i2−i2i2−i22i−2i2i−2i00002i−2i00i2−i2000000i2−i2i2−i22−22−200000000002−20
χ462-2-22-222-20002-22-2002-22-200000i2−i2i2−i2−2i2i−2i2i0000−2i2i00i2−i2000000i2−i2i2−i2−22−220000000000−220
χ472-2-22-222-20002-22-2002-22-200000−i2i2−i2i22i−2i2i−2i00002i−2i00−i2i2000000−i2i2−i2i2−22−220000000000−220
χ482-2-22-222-20002-22-2002-22-200000−i2i2−i2i2−2i2i−2i2i0000−2i2i00−i2i2000000−i2i2−i2i22−22−200000000002−20
χ492-2-22-222-20002-22-200-22-2200000i2−i2i2−i22i−2i2i−2i0000−2i2i00i2−i2000000−i2i2−i2i22−22−20000000000−220
χ502-2-22-222-20002-22-200-22-2200000i2−i2i2−i2−2i2i−2i2i00002i−2i00i2−i2000000−i2i2−i2i2−22−2200000000002−20
χ512-2-22-222-20002-22-200-22-2200000−i2i2−i2i22i−2i2i−2i0000−2i2i00−i2i2000000i2−i2i2−i2−22−2200000000002−20
χ522-2-22-222-20002-22-200-22-2200000−i2i2−i2i2−2i2i−2i2i00002i−2i00−i2i2000000i2−i2i2−i22−22−20000000000−220
χ5344444444-4-4-4-4-4-4-4-44000000004000000000000000000000000000000000000000000000
χ5444-444-4-4-44-440000-4000000000000002222−22−220000000000−22220000000000000000000000000
χ5544-444-4-4-44-440000-400000000000000−22−222222000000000022−220000000000000000000000000
χ5644-4-4-44-440004-4-44000000000000000000000000000000000002i2−2i2−2i22i200000000000000000
χ5744-4-4-44-440004-4-4400000000000000000000000000000000000−2i22i22i2−2i200000000000000000
χ5844-4-4-44-44000-444-4004i−4i−4i4i00000000000000000000000000000000000000000000000000
χ5944-4-4-44-44000-444-400−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ604-444-4-4-4400000000000000000022−22−22222i2−2i2−2i22i200000000000000000000−2i2i2i−2i0000000000000
χ614-444-4-4-4400000000000000000022−22−2222−2i22i22i2−2i2000000000000000000002i−2i−2i2i0000000000000
χ624-444-4-4-44000000000000000000−222222−222i2−2i2−2i22i2000000000000000000002i−2i−2i2i0000000000000
χ634-444-4-4-44000000000000000000−222222−22−2i22i22i2−2i200000000000000000000−2i2i2i−2i0000000000000
χ644-44-444-4-4-44444-4-4-4400000000-4000000000000000000000000000000000000000000000
χ654-4-44-444-4000-44-44000000000002i2−2i22i2−2i2000000000000−2i22i2000000000000000000000000000
χ664-4-44-444-4000-44-4400000000000−2i22i2−2i22i20000000000002i2−2i2000000000000000000000000000
χ674-4-4-44-44444-40000-40000000000000000000000000000002i2−2i2−2i22i2000000000000000000000
χ684-4-4-44-44444-40000-4000000000000000000000000000000−2i22i22i2−2i2000000000000000000000
χ694-4-4-44-444-4-4400004000004-4-440000000000000000000000000000000000000000000000
χ704-4-4-44-444-4-440000400000-444-40000000000000000000000000000000000000000000000
χ71888-8-8-88-8000000000000000000000000000000000000000000000000000000000000000

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