Finite Group Databasebeta

← Group #256651

Character table — Group #256651

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222444444444444444444444444888888888888161616161616161616161616161616161616
order12222222444444444444224444448888888888888888444444444444244444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-111-11111-1-1-1-1-1-1-1-1
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1111-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11111-1-1-111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-1-1111-1-1111111-1-1-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111111111
χ91111111111-1-1-1-1111111-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-11-111111-1-111-1-111-1-1
χ101111111111-1-1-1-1111111-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111
χ111111111111-1-1-1-1111111-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-11-1-11-1-111-1-11111-1-1
χ121111111111-1-1-1-1111111-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11-1111-111-1-1-1-111-1-111
χ131111111111-1-1-1-1111111-1-11-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1-11-1-1-111111-1-111-1-111
χ141111111111-1-1-1-1111111-1-11-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-111-1-1-1-1-1-1-11111-1-1
χ151111111111-1-1-1-1111111-1-11-1-1-1-11-1-1-1-1-1-1-1-111111111-1-11111-1-11111-1-11111-1-1-1-111-1-1-1-111
χ161111111111-1-1-1-1111111-1-11-1-1-1-11-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-11-11-1-1-1111111-1-111-1-1
χ1722222222222222-2-222-2-222-2-2-2-2-2-20000000000000000000022220000-20000-2000000000000
χ1822222222222222-2-222-2-222-2-2-2-2-2-200000000000000000000-2-2-2-20000200002000000000000
χ192222222222-2-2-2-2-2-222-2-2-2-2-22222-20000000000000000000022-2-2000020000-2000000000000
χ202222222222-2-2-2-2-2-222-2-2-2-2-22222-200000000000000000000-2-2220000-200002000000000000
χ2122222222-2-2222222-2-222-2-2-222-2-2-200000000000000002222000000000-2-2000000000000000
χ2222222222-2-2222222-2-222-2-2-222-2-2-20000000000000000-2-2-2-200000000022000000000000000
χ2322222222-2-22222-2-2-2-2-2-2-2-22-2-222200000000000000000000000022-2-20000002-20000000000
χ2422222222-2-22222-2-2-2-2-2-2-2-22-2-2222000000000000000000000000-2-222000000-220000000000
χ2522222222-2-2-2-2-2-222-2-22222-2-2-222-2000000000000000022-2-2000000000-22000000000000000
χ2622222222-2-2-2-2-2-222-2-22222-2-2-222-20000000000000000-2-2220000000002-2000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-222222-2-2200000000000000000000000022-2-2000000-220000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222222-2-22000000000000000000000000-2-2220000002-20000000000
χ2922-22-22-2-22-200002-22-22-200-200002000000002222-2-2-2-2000000002i−2i2i−2i0002i−2i0000000000000
χ3022-22-22-2-22-200002-22-22-200-200002000000002222-2-2-2-200000000−2i2i−2i2i000−2i2i0000000000000
χ3122-22-22-2-22-200002-22-22-200-20000200000000-2-2-2-22222000000002i−2i2i−2i000−2i2i0000000000000
χ3222-22-22-2-22-200002-22-22-200-20000200000000-2-2-2-2222200000000−2i2i−2i2i0002i−2i0000000000000
χ3322-22-22-2-2-220000-22-22-2200-2000022222-2-2-2-200000000000000002i−2i−2i2i000000002i−2i00000000
χ3422-22-22-2-2-220000-22-22-2200-2000022222-2-2-2-20000000000000000−2i2i2i−2i00000000−2i2i00000000
χ3522-22-22-2-2-220000-22-22-2200-200002-2-2-2-2222200000000000000002i−2i−2i2i00000000−2i2i00000000
χ3622-22-22-2-2-220000-22-22-2200-200002-2-2-2-222220000000000000000−2i2i2i−2i000000002i−2i00000000
χ3722-2-2-2-2222222-2-200-2-2002-200000022−2−222−2−222−2−222−2−200002i−2i2i−2i000000000000000000i2−i2i2−i2
χ3822-2-2-2-2222222-2-200-2-2002-200000022−2−222−2−222−2−222−2−20000−2i2i−2i2i000000000000000000−i2i2−i2i2
χ3922-2-2-2-2222222-2-200-2-2002-2000000−2−222−2−222−2−222−2−22200002i−2i2i−2i000000000000000000−i2i2−i2i2
χ4022-2-2-2-2222222-2-200-2-2002-2000000−2−222−2−222−2−222−2−2220000−2i2i−2i2i000000000000000000i2−i2i2−i2
χ4122-2-2-2-22222-2-22200-2-200-2200000022−2−222−2−2−2−222−2−22200002i−2i−2i2i000000000000000000i2−i2−i2i2
χ4222-2-2-2-22222-2-22200-2-200-2200000022−2−222−2−2−2−222−2−2220000−2i2i2i−2i000000000000000000−i2i2i2−i2
χ4322-2-2-2-22222-2-22200-2-200-22000000−2−222−2−22222−2−222−2−200002i−2i−2i2i000000000000000000−i2i2i2−i2
χ4422-2-2-2-22222-2-22200-2-200-22000000−2−222−2−22222−2−222−2−20000−2i2i2i−2i000000000000000000i2−i2−i2i2
χ452-22-2-222-2002i−2i2i−2i-22002-20002i−2i000i2−i2i2−i2i2−i2i2−i22−22−22−22−22-22i−2i000000000000000000i2−i22−20000
χ462-22-2-222-2002i−2i2i−2i-22002-20002i−2i000i2−i2i2−i2i2−i2i2−i22−22−22−22−2-22−2i2i000000000000000000−i2i2−220000
χ472-22-2-222-2002i−2i2i−2i-22002-20002i−2i000−i2i2−i2i2−i2i2−i2i2−22−22−22−222-22i−2i000000000000000000−i2i2−220000
χ482-22-2-222-2002i−2i2i−2i-22002-20002i−2i000−i2i2−i2i2−i2i2−i2i2−22−22−22−22-22−2i2i000000000000000000i2−i22−20000
χ492-22-2-222-200−2i2i−2i2i-22002-2000−2i2i000i2−i2i2−i2i2−i2i2−i2−22−22−22−222-2−2i2i000000000000000000i2−i2−220000
χ502-22-2-222-200−2i2i−2i2i-22002-2000−2i2i000i2−i2i2−i2i2−i2i2−i2−22−22−22−22-222i−2i000000000000000000−i2i22−20000
χ512-22-2-222-200−2i2i−2i2i-22002-2000−2i2i000−i2i2−i2i2−i2i2−i2i22−22−22−22−22-2−2i2i000000000000000000−i2i22−20000
χ522-22-2-222-200−2i2i−2i2i-22002-2000−2i2i000−i2i2−i2i2−i2i2−i2i22−22−22−22−2-222i−2i000000000000000000i2−i2−220000
χ53444-44-4-4-44-4000000-440000000000000000002222−22−22−22−222222000000000000000000000000000000
χ54444-44-4-4-44-4000000-44000000000000000000−22−2222222222−22−22000000000000000000000000000000
χ55444-44-4-4-4-440000004-400000000002222−22−22−22−22222200000000000000000000000000000000000000
χ56444-44-4-4-4-440000004-40000000000−22−2222222222−22−2200000000000000000000000000000000000000
χ5744-44-44-4-44-40000-444-4-440040000-40000000000000000000000000000000000000000000000
χ5844-44-44-4-4-4400004-4-444-40040000-40000000000000000000000000000000000000000000000
χ5944-4-4-4-444-4-444-4-4004400-440000000000000000000000000000000000000000000000000000
χ6044-4-4-4-444-4-4-4-4440044004-40000000000000000000000000000000000000000000000000000
χ614-444-4-4-44000000000000000004i−4i02i−2i−2i2i−2i2i2i−2i2-2-22-222-2000000000000000000000000000000
χ624-444-4-4-44000000000000000004i−4i0−2i2i2i−2i2i−2i−2i2i-222-22-2-22000000000000000000000000000000
χ634-444-4-4-4400000000000000000−4i4i02i−2i−2i2i−2i2i2i−2i-222-22-2-22000000000000000000000000000000
χ644-444-4-4-4400000000000000000−4i4i0−2i2i2i−2i2i−2i−2i2i2-2-22-222-2000000000000000000000000000000
χ654-44-4-444-4004i−4i4i−4i4-400-44000−4i4i0000000000000000000000000000000000000000000000000
χ664-44-4-444-400−4i4i−4i4i4-400-440004i−4i0000000000000000000000000000000000000000000000000
χ674-4-444-44-4004i−4i−4i4i000000000000002i−2i−2i2i2i−2i−2i2i2-2-222-2-22000000000000000000000000000000
χ684-4-444-44-4004i−4i−4i4i00000000000000−2i2i2i−2i−2i2i2i−2i-222-2-222-2000000000000000000000000000000
χ694-4-444-44-400−4i4i4i−4i000000000000002i−2i−2i2i2i−2i−2i2i-222-2-222-2000000000000000000000000000000
χ704-4-444-44-400−4i4i4i−4i00000000000000−2i2i2i−2i−2i2i2i−2i2-2-222-2-22000000000000000000000000000000
χ714-4-4-444-440000004400-4-4000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000000000000000
χ724-4-4-444-440000004400-4-400000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000000000000000
χ734-4-4-444-44000000-4-40044000000000000000022−2222−22−2222−2222000000000000000000000000000000
χ744-4-4-444-44000000-4-400440000000000000000−2222−222222−2222−22000000000000000000000000000000

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