Finite Group Databasebeta

← Group #269773

Character table — Group #269773

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888882222224488888888888888884444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-11111-1-11111-1-11111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-111111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-1-111111
χ5111111111111111111111-1-1-1-111111111111-1-111-1-111111111-1-1-1-11111-1-1-1-1-11-1-111-1-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1111
χ7111111111111111111111-1-1-1-11-1-1-1-1111111-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111-1-11-1-1-1-1111
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111111-1-1-11111-1-1-1
χ911111111111111111-1-1-1-11111111111111-1-111-1-1111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-111-1
χ1011111111111111111-1-1-1-1111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111111-1-11
χ1111111111111111111-1-1-1-111111-1-1-1-11111-1-111-1-1-1-1-1-11111111111-1-1-1-1-111-1-1-1-1-111-1-11
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-111-1-1111-1-111-1
χ1311111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-11111-111-1-1-1-11
χ1411111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-111111-1-11111-1
χ1511111111111111111-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11-1-111-1111111-1
χ1611111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111111-1-1111-1-1-1-1-1-11
χ17222222222-2-22-222-2-200002222-22222000000-2-20022-2-200000000000000-2000000000000
χ18222222222-2-22-222-2-200002222-2-2-2-2-2000000-2-200-2-222000000000000002000000000000
χ19222222222-2-22-222-2-20000-2-2-2-2-222220000002200-2-2-2-2000000000000002000000000000
χ20222222222-2-22-222-2-20000-2-2-2-2-2-2-2-2-20000002200222200000000000000-2000000000000
χ2122222222-222-22-2-22-222220000-200002222-2-200220000-2-200000000000000000-20000000
χ2222222222-222-22-2-22-222220000-20000-2-2-2-2-2-200-2-20000220000000000000000020000000
χ2322222222-222-22-2-22-2-2-2-2-20000-2000022222200-2-20000-2-20000000000000000020000000
χ2422222222-222-22-2-22-2-2-2-2-20000-20000-2-2-2-222002200002200000000000000000-20000000
χ25222-2-22-2-2-200-20220000002i2i−2i−2i022-2-222−2−20000002i−2i002−20000i2i2−i2−i222−2−20000000000i2−i20
χ26222-2-22-2-2-200-20220000002i2i−2i−2i022-2-2−2−2220000002i−2i00−220000−i2−i2i2i2−2−2220000000000−i2i20
χ27222-2-22-2-2-200-20220000002i2i−2i−2i0-2-22222−2−2000000−2i2i002−20000i2i2−i2−i2−2−2220000000000−i2i20
χ28222-2-22-2-2-200-20220000002i2i−2i−2i0-2-222−2−222000000−2i2i00−220000−i2−i2i2i222−2−20000000000i2−i20
χ29222-2-22-2-2-200-2022000000−2i−2i2i2i022-2-222−2−2000000−2i2i002−20000−i2−i2i2i222−2−20000000000−i2i20
χ30222-2-22-2-2-200-2022000000−2i−2i2i2i022-2-2−2−222000000−2i2i00−220000i2i2−i2−i2−2−2220000000000i2−i20
χ31222-2-22-2-2-200-2022000000−2i−2i2i2i0-2-22222−2−20000002i−2i002−20000−i2−i2i2i2−2−2220000000000i2−i20
χ32222-2-22-2-2-200-2022000000−2i−2i2i2i0-2-222−2−2220000002i−2i00−220000i2i2−i2−i222−2−20000000000−i2i20
χ332-222-2-2-2202-20200-202i2i−2i−2i000002−22−22i−2i2i−2i00002-2002−200i2i2−i2−i20000i2−i2i2−i2000000002−2000
χ342-222-2-2-2202-20200-202i2i−2i−2i000002−22−2−2i2i−2i2i0000-22002−200i2i2−i2−i20000−i2i2−i2i200000000−22000
χ352-222-2-2-2202-20200-202i2i−2i−2i00000−22−222i−2i2i−2i00002-200−2200−i2−i2i2i20000−i2i2−i2i200000000−22000
χ362-222-2-2-2202-20200-202i2i−2i−2i00000−22−22−2i2i−2i2i0000-2200−2200−i2−i2i2i20000i2−i2i2−i2000000002−2000
χ372-222-2-2-2202-20200-20−2i−2i2i2i000002−22−22i−2i2i−2i0000-22002−200−i2−i2i2i20000i2−i2i2−i200000000−22000
χ382-222-2-2-2202-20200-20−2i−2i2i2i000002−22−2−2i2i−2i2i00002-2002−200−i2−i2i2i20000−i2i2−i2i2000000002−2000
χ392-222-2-2-2202-20200-20−2i−2i2i2i00000−22−222i−2i2i−2i0000-2200−2200i2i2−i2−i20000−i2i2−i2i2000000002−2000
χ402-222-2-2-2202-20200-20−2i−2i2i2i00000−22−22−2i2i−2i2i00002-200−2200i2i2−i2−i20000i2−i2i2−i200000000−22000
χ412-2-2-2-2222222-2-22-2-2200002-22-2-200000000002-2000000002i−2i2i−2i0000000002i−2i0000000000
χ422-2-2-2-2222222-2-22-2-2200002-22-2-200000000002-200000000−2i2i−2i2i000000000−2i2i0000000000
χ432-2-2-2-2222222-2-22-2-220000-22-22-20000000000-22000000002i−2i2i−2i000000000−2i2i0000000000
χ442-2-2-2-2222222-2-22-2-220000-22-22-20000000000-2200000000−2i2i−2i2i0000000002i−2i0000000000
χ452-2-2-2-22222-2-2-222-22-22-22-22-22-22000000002-2-22000000000000000000000002-200000000
χ462-2-2-2-22222-2-2-222-22-22-22-2-22-222000000002-22-200000000000000000000000-2200000000
χ472-2-2-2-22222-2-2-222-22-2-22-222-22-2200000000-22-2200000000000000000000000-2200000000
χ482-2-2-2-22222-2-2-222-22-2-22-22-22-22200000000-222-2000000000000000000000002-200000000
χ492-2-2-2-2222-2-2-222-22222-22-20000-200000000-22000000000000002-22-200000000002-200000
χ502-2-2-2-2222-2-2-222-22222-22-20000-200000000-2200000000000000-22-220000000000-2200000
χ512-2-2-2-2222-2-2-222-2222-22-220000-2000000002-2000000000000002-22-20000000000-2200000
χ522-2-2-2-2222-2-2-222-2222-22-220000-2000000002-200000000000000-22-2200000000002-200000
χ5344444444-4-4-4-4-4-4-4-44000000004000000000000000000000000000000000000000000000
χ54444-4-44-4-440040-4-40000000000000002222−22−220000000000−22220000000000000000000000000
χ55444-4-44-4-440040-4-4000000000000000−22−222222000000000022−220000000000000000000000000
χ5644-4-44-4-4404-40-400400000000000000000000000000000022−22−2222000000000000000000000
χ5744-4-44-4-4404-40-4004000000000000000000000000000000−222222−22000000000000000000000
χ5844-4-44-4-440-440400-404i−4i−4i4i00000000000000000000000000000000000000000000000000
χ5944-4-44-4-440-440400-40−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ604-444-4-4-440-440-4004000000000022−2222−22000000000000−2222000000000000000000000000000
χ614-444-4-4-440-440-40040000000000−2222−222200000000000022−22000000000000000000000000000
χ624-44-44-44-400000000000000000022−22−22222i2−2i2−2i22i2000000000000000000002i−2i−2i2i0000000000000
χ634-44-44-44-400000000000000000022−22−2222−2i22i22i2−2i200000000000000000000−2i2i2i−2i0000000000000
χ644-44-44-44-4000000000000000000−222222−222i2−2i2−2i22i200000000000000000000−2i2i2i−2i0000000000000
χ654-44-44-44-4000000000000000000−222222−22−2i22i22i2−2i2000000000000000000002i−2i−2i2i0000000000000
χ664-4-4444-4-4400-40-44000000000000000000000000000000000002i2−2i2−2i22i200000000000000000
χ674-4-4444-4-4400-40-4400000000000000000000000000000000000−2i22i22i2−2i200000000000000000
χ684-4-4444-4-4-400404-40000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ694-4-4444-4-4-400404-4000000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ704-4-4-4-4444-4444-4-44-4-4000000004000000000000000000000000000000000000000000000
χ7188-88-8-88-8000000000000000000000000000000000000000000000000000000000000000

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