Finite Group Databasebeta

← Group #310195

Character table — Group #310195

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888884444444488888888888888884444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-1111-1-111-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111-1-1111111-1-1111111-1-1-1-1-1-1-1-1-11111-1-11-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-1-111111
χ511111111111111111111-1-1-1-1111111111111-1-111-1-111111111-1-1-1-111111-1-1-1-1-1-1-111-1-1-1
χ611111111111111111111-1-1-1-1111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-11-1-1111
χ711111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-111-1-1-1111
χ811111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-11111111-1-1-1
χ91111111111111111-1-1-1-111111111111111-1-111-1-11111-1-1-1-11111111111-1-1-1-1-1-1-11-1-111-1
χ101111111111111111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1111111-1-11111-1-1-1-1-1-1-111-1-1-111-1-11
χ111111111111111111-1-1-1-1111111-1-1-1-111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-111111-1-11
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111111-1-11111-1-1-111-1
χ131111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1111111-1-1-1-1-11
χ141111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-111-1-11111111-1
χ151111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111-1-1-11111-1
χ161111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-111111111111-1-1-1-11-1-1-1-11
χ17222222222-222-2-2-2222220000-2-2222200002200-2-200-2-200000000000000-2000000000000
χ18222222222-222-2-2-2222220000-2-2-2-2-2-20000-2-200-2-20022000000000000002000000000000
χ19222222222-222-2-2-22-2-2-2-20000-2-222220000-2-2002200-2-2000000000000002000000000000
χ20222222222-222-2-2-22-2-2-2-20000-2-2-2-2-2-20000220022002200000000000000-2000000000000
χ2122222222-22-2-2222-200002222-2-20000222200-2-20022000000-2-2000000000000000-200000
χ2222222222-22-2-2222-200002222-2-20000-2-2-2-200-2-200-2-200000022000000000000000200000
χ2322222222-22-2-2222-20000-2-2-2-2-2-200002222002200-2-2000000-2-2000000000000000200000
χ2422222222-22-2-2222-20000-2-2-2-2-2-20000-2-2-2-20022002200000022000000000000000-200000
χ2522-2-222-2-2-202-200022i2i−2i−2i0000002i2i−2i−2i22−2−22-200000000i2i2−i2−i22−20000i2i2−i2−i2000000002−2000
χ2622-2-222-2-2-202-200022i2i−2i−2i0000002i2i−2i−2i−2−2222-200000000−i2−i2i2i2−220000−i2−i2i2i200000000−22000
χ2722-2-222-2-2-202-200022i2i−2i−2i000000−2i−2i2i2i22−2−2-2200000000i2i2−i2−i22−20000−i2−i2i2i200000000−22000
χ2822-2-222-2-2-202-200022i2i−2i−2i000000−2i−2i2i2i−2−222-2200000000−i2−i2i2i2−220000i2i2−i2−i2000000002−2000
χ2922-2-222-2-2-202-20002−2i−2i2i2i0000002i2i−2i−2i22−2−2-2200000000−i2−i2i2i22−20000i2i2−i2−i200000000−22000
χ3022-2-222-2-2-202-20002−2i−2i2i2i0000002i2i−2i−2i−2−222-2200000000i2i2−i2−i2−220000−i2−i2i2i2000000002−2000
χ3122-2-222-2-2-202-20002−2i−2i2i2i000000−2i−2i2i2i22−2−22-200000000−i2−i2i2i22−20000−i2−i2i2i2000000002−2000
χ3222-2-222-2-2-202-20002−2i−2i2i2i000000−2i−2i2i2i−2−2222-200000000i2i2−i2−i2−220000i2i2−i2−i200000000−22000
χ332-22-2-222-20200-2-22000002i2i−2i−2i00i2−i2i2−i22i−2i2i−2i0000002-2i2−i200000022−2−22−22−20000000000i2−i20
χ342-22-2-222-20200-2-22000002i2i−2i−2i00i2−i2i2−i2−2i2i−2i2i000000-22i2−i200000022−2−2−22−220000000000−i2i20
χ352-22-2-222-20200-2-22000002i2i−2i−2i00−i2i2−i2i22i−2i2i−2i0000002-2−i2i2000000−2−222−22−220000000000−i2i20
χ362-22-2-222-20200-2-22000002i2i−2i−2i00−i2i2−i2i2−2i2i−2i2i000000-22−i2i2000000−2−2222−22−20000000000i2−i20
χ372-22-2-222-20200-2-2200000−2i−2i2i2i00i2−i2i2−i22i−2i2i−2i000000-22i2−i2000000−2−2222−22−20000000000−i2i20
χ382-22-2-222-20200-2-2200000−2i−2i2i2i00i2−i2i2−i2−2i2i−2i2i0000002-2i2−i2000000−2−222−22−220000000000i2−i20
χ392-22-2-222-20200-2-2200000−2i−2i2i2i00−i2i2−i2i22i−2i2i−2i000000-22−i2i200000022−2−2−22−220000000000i2−i20
χ402-22-2-222-20200-2-2200000−2i−2i2i2i00−i2i2−i2i2−2i2i−2i2i0000002-2−i2i200000022−2−22−22−20000000000−i2i20
χ412-2-2-22-22222-2-2-22-2200002i−2i2i−2i2-200000000002i−2i0000002-22-200000000000002i−2i00000000
χ422-2-2-22-22222-2-2-22-2200002i−2i2i−2i2-200000000002i−2i000000-22-220000000000000−2i2i00000000
χ432-2-2-22-22222-2-2-22-220000−2i2i−2i2i2-20000000000−2i2i0000002-22-20000000000000−2i2i00000000
χ442-2-2-22-22222-2-2-22-220000−2i2i−2i2i2-20000000000−2i2i000000-22-2200000000000002i−2i00000000
χ452-2-2-22-222-2222-22-2-22i−2i2i−2i2i−2i2i−2i-220000000000−2i2i2i−2i00000000000000000002-20000000000
χ462-2-2-22-222-2222-22-2-22i−2i2i−2i−2i2i−2i2i-2200000000002i−2i2i−2i0000000000000000000-220000000000
χ472-2-2-22-222-2222-22-2-2−2i2i−2i2i2i−2i2i−2i-220000000000−2i2i−2i2i0000000000000000000-220000000000
χ482-2-2-22-222-2222-22-2-2−2i2i−2i2i−2i2i−2i2i-2200000000002i−2i−2i2i00000000000000000002-20000000000
χ492-2-2-22-222-2-2222-22-22i−2i2i−2i00002-2000000000000−2i2i00000000002i−2i2i−2i0000000002-2000000
χ502-2-2-22-222-2-2222-22-22i−2i2i−2i00002-2000000000000−2i2i0000000000−2i2i−2i2i000000000-22000000
χ512-2-2-22-222-2-2222-22-2−2i2i−2i2i00002-20000000000002i−2i00000000002i−2i2i−2i000000000-22000000
χ522-2-2-22-222-2-2222-22-2−2i2i−2i2i00002-20000000000002i−2i0000000000−2i2i−2i2i0000000002-2000000
χ5344444444-4-4-4-4-4-4-4-40000000044000000000000000000000000000000000000000000000
χ5444-44-4-44-404004-4-4000004-4-4400000000000000000000000000000000000000000000000
χ5544-44-4-44-404004-4-400000-444-400000000000000000000000000000000000000000000000
χ5644-44-4-44-40-400-444000000000000000000000000000000000002i2−2i2−2i22i200000000000000000
χ5744-44-4-44-40-400-44400000000000000000000000000000000000−2i22i22i2−2i200000000000000000
χ5844-4-444-4-440-44000-4000000000000002222−22−2200000000000000−2222000000000000000000000
χ5944-4-444-4-440-44000-400000000000000−22−2222220000000000000022−22000000000000000000000
χ604-4444-4-4-4404-4000-44-4-44000000000000000000000000000000000000000000000000000
χ614-4444-4-4-4404-4000-4-444-4000000000000000000000000000000000000000000000000000
χ624-4444-4-4-4-40-44000400000000000000000000000000002i2−2i2−2i22i200000000000000000000000
χ634-4444-4-4-4-40-4400040000000000000000000000000000−2i22i22i2−2i200000000000000000000000
χ644-44-4-444-40-40044-4000000000002i2−2i22i2−2i2000000000000−2i22i2000000000000000000000000000
χ654-44-4-444-40-40044-400000000000−2i22i2−2i22i20000000000002i2−2i2000000000000000000000000000
χ664-4-44-44-4400000000000000000022−22−22222i2−2i2−2i22i200000000000000000000−2i2i2i−2i0000000000000
χ674-4-44-44-4400000000000000000022−22−2222−2i22i22i2−2i2000000000000000000002i−2i−2i2i0000000000000
χ684-4-44-44-44000000000000000000−222222−222i2−2i2−2i22i2000000000000000000002i−2i−2i2i0000000000000
χ694-4-44-44-44000000000000000000−222222−22−2i22i22i2−2i200000000000000000000−2i2i2i−2i0000000000000
χ704-4-4-44-4444-4-4-44-44400000000-44000000000000000000000000000000000000000000000
χ71888-8-8-8-88000000000000000000000000000000000000000000000000000000000000000

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