Finite Group Databasebeta

← Group #311331

Character table — Group #311331

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444488888888888888888888888888161616161616161616163232
order12222222444444444444448888888844444444448888888888888888244444888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1111-1
χ61111111111111111111111-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-111-1-111-1-1-11
χ71111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-11-1-11111-1-1-11
χ81111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111-111-1-1-1-1111-1
χ911111111111111111-1-1-1-1111111111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111
χ1011111111111111111-1-1-1-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1
χ1111111111111111111-1-1-1-1111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ1211111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111
χ1311111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1111-1-111-1-11-1
χ1411111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-111111-1-1-111-1-111-11
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-1-1111-1-1-1-111-11
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-11-1-1-11111-1-11-1
χ17222222222-222-2-2-22-20000-22222-2-2-2-200000022220000000000000000-2-20000000000
χ18222222222-222-2-2-22-20000-22222-2-2-2-2000000-2-2-2-20000000000000000220000000000
χ19222222222-222-2-2-22-20000-2-2-2-2-2222200000022-2-200000000000000002-20000000000
χ20222222222-222-2-2-22-20000-2-2-2-2-22222000000-2-2220000000000000000-220000000000
χ2122222222-22-2-2222-2-22222-200000000-2-222-2-2000022-2-2000000000000000000000000
χ2222222222-22-2-2222-2-22222-200000000-2-2-2-2220000-2-222000000000000000000000000
χ2322222222-22-2-2222-2-2-2-2-2-2-2000000002222-2-20000-2-222000000000000000000000000
χ2422222222-22-2-2222-2-2-2-2-2-2-20000000022-2-222000022-2-2000000000000000000000000
χ25222-2-2-2-2222-2-2-22-22-2000022i2i−2i−2i2i2i−2i−2i00000000000000000000000000002i−2i2-2000000
χ26222-2-2-2-2222-2-2-22-22-2000022i2i−2i−2i2i2i−2i−2i0000000000000000000000000000−2i2i-22000000
χ27222-2-2-2-2222-2-2-22-22-200002−2i−2i2i2i−2i−2i2i2i00000000000000000000000000002i−2i-22000000
χ28222-2-2-2-2222-2-2-22-22-200002−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000−2i2i2-2000000
χ29222-2-2-2-222-2-2-22-22222i2i−2i−2i-22i2i−2i−2i−2i−2i2i2i2i−2i00000000000022-2-200000000000000000000
χ30222-2-2-2-222-2-2-22-22222i2i−2i−2i-2−2i−2i2i2i2i2i−2i−2i2i−2i000000000000-2-22200000000000000000000
χ31222-2-2-2-222-2-2-22-2222−2i−2i2i2i-22i2i−2i−2i−2i−2i2i2i−2i2i000000000000-2-22200000000000000000000
χ32222-2-2-2-222-2-2-22-2222−2i−2i2i2i-2−2i−2i2i2i2i2i−2i−2i−2i2i00000000000022-2-200000000000000000000
χ33222-2-2-2-22-2-2222-22-2-22i2i−2i−2i200000000−2i2i00000000000000002i2i−2i−2i22-2-2000000000000
χ34222-2-2-2-22-2-2222-22-2-22i2i−2i−2i200000000−2i2i0000000000000000−2i−2i2i2i-2-222000000000000
χ35222-2-2-2-22-2-2222-22-2-2−2i−2i2i2i2000000002i−2i00000000000000002i2i−2i−2i-2-222000000000000
χ36222-2-2-2-22-2-2222-22-2-2−2i−2i2i2i2000000002i−2i0000000000000000−2i−2i2i2i22-2-2000000000000
χ372-2-222-2-220200-2-22002i−2i2i−2i0i2−i2i2−i2i2−i2i2−i2002-20000002i−2i002−22−2i2−i2i2−i22−22−2000000000000
χ382-2-222-2-220200-2-22002i−2i2i−2i0i2−i2i2−i2i2−i2i2−i200-22000000−2i2i002−22−2−i2i2−i2i2−22−22000000000000
χ392-2-222-2-220200-2-22002i−2i2i−2i0−i2i2−i2i2−i2i2−i2i2002-20000002i−2i00−22−22−i2i2−i2i2−22−22000000000000
χ402-2-222-2-220200-2-22002i−2i2i−2i0−i2i2−i2i2−i2i2−i2i200-22000000−2i2i00−22−22i2−i2i2−i22−22−2000000000000
χ412-2-222-2-220200-2-2200−2i2i−2i2i0i2−i2i2−i2i2−i2i2−i2002-2000000−2i2i00−22−22i2−i2i2−i2−22−22000000000000
χ422-2-222-2-220200-2-2200−2i2i−2i2i0i2−i2i2−i2i2−i2i2−i200-220000002i−2i00−22−22−i2i2−i2i22−22−2000000000000
χ432-2-222-2-220200-2-2200−2i2i−2i2i0−i2i2−i2i2−i2i2−i2i2002-2000000−2i2i002−22−2−i2i2−i2i22−22−2000000000000
χ442-2-222-2-220200-2-2200−2i2i−2i2i0−i2i2−i2i2−i2i2−i2i200-220000002i−2i002−22−2i2−i2i2−i2−22−22000000000000
χ452-2-2-2-22220-200-222002-2-2202−2−22−222−200002-20000002-22−2−222−2−222−2−22000000000000
χ462-2-2-2-22220-200-222002-2-2202−2−22−222−20000-22000000-222−2−22−222−2−222−2000000000000
χ472-2-2-2-22220-200-222002-2-220−222−22−2−2200002-20000002-2−222−2−222−2−222−2000000000000
χ482-2-2-2-22220-200-222002-2-220−222−22−2−220000-22000000-22−222−22−2−222−2−22000000000000
χ492-2-2-2-22220-200-22200-222-202−2−22−222−200002-2000000-22−222−22−2−22−222−2000000000000
χ502-2-2-2-22220-200-22200-222-202−2−22−222−20000-220000002-2−222−2−222−22−2−22000000000000
χ512-2-2-2-22220-200-22200-222-20−222−22−2−2200002-2000000-222−2−22−222−22−2−22000000000000
χ522-2-2-2-22220-200-22200-222-20−222−22−2−220000-220000002-22−2−222−2−22−222−2000000000000
χ5344444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000000
χ54444-4-4-4-44-4444-44-4-440000-40000000000000000000000000000000000000000000000
χ5544-44-44-4-4404-4000-400000000000000000000000000000000000000000000000022−2200
χ5644-44-44-4-4404-4000-4000000000000000000000000000000000000000000000000−222200
χ5744-44-44-4-4-40-440004000000000000000000004i−4i000000000000000000000000000000
χ5844-44-44-4-4-40-44000400000000000000000000−4i4i000000000000000000000000000000
χ5944-4-44-44-440-44000-4000000000000000000000000000000000000000000000022−220000
χ6044-4-44-44-440-44000-40000000000000000000000000000000000000000000000−22220000
χ6144-4-44-44-4-404-4000400000000000000000000004i−4i0000000000000000000000000000
χ6244-4-44-44-4-404-400040000000000000000000000−4i4i0000000000000000000000000000
χ634-4-444-4-440-40044-400000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000000000000000
χ644-4-444-4-440-40044-40000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000000000000000
χ654-4-4-4-444404004-4-4000000022−22−222222−22−222200000000000000000000000000000000000000
χ664-4-4-4-444404004-4-40000000−222222−22−222222−2200000000000000000000000000000000000000
χ678-888-8-88-8000000000000000000000000000000000000000000000000000000000000
χ688-88-888-8-8000000000000000000000000000000000000000000000000000000000000

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