Finite Group Databasebeta

← Group #309049

Character table — Group #309049

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444488888888888888888888888888161616161616161616163232
order12222222444444444444448888888844444444448888888888888888224444888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
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
χ51111111111111111111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-11-1
χ61111111111111111111111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-111-11
χ71111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1111-1-111-11
χ81111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111111-1-1-111-1-11-1
χ911111111111111111-1-1-1-1111111111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11-1-11-1-1-1-111
χ1011111111111111111-1-1-1-1111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-111-11111-1-1
χ1111111111111111111-1-1-1-1111111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-11-1-111111-1-1
χ1211111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-111-1-1-1-1-111
χ1311111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1111111-1-1-11-1-1111-1
χ1411111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1111-111-1-1-11
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-111-1-1-1111-1-1-11
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1111-1-1-1111-1
χ172222222222-2-2-222-2-22222-200000000-2-22200-2-20022-2-2000000000000000000000000
χ182222222222-2-2-222-2-22222-200000000-2-2-2-2002200-2-222000000000000000000000000
χ192222222222-2-2-222-2-2-2-2-2-2-200000000222200-2-200-2-222000000000000000000000000
χ202222222222-2-2-222-2-2-2-2-2-2-20000000022-2-200220022-2-2000000000000000000000000
χ2122222222-2-2222-2-22-20000-22222-2-2-2-20000220022000000000000000000-200-2000000
χ2222222222-2-2222-2-22-20000-22222-2-2-2-20000-2-200-2-20000000000000000002002000000
χ2322222222-2-2222-2-22-20000-2-2-2-2-2222200002200-2-2000000000000000000200-2000000
χ2422222222-2-2222-2-22-20000-2-2-2-2-222220000-2-20022000000000000000000-2002000000
χ25222-2-22-2-222-222-2-2-220000-222-2-222-2-2000000000000000000000000002-202-20000000
χ26222-2-22-2-222-222-2-2-220000-222-2-222-2-200000000000000000000000000-220-220000000
χ27222-2-22-2-222-222-2-2-220000-2-2-222-2-222000000000000000000000000002-20-220000000
χ28222-2-22-2-222-222-2-2-220000-2-2-222-2-22200000000000000000000000000-2202-20000000
χ29222-2-22-2-2-2-22-2-222222i2i−2i−2i-2000000002i−2i000000000000000022-2-22i2i−2i−2i000000000000
χ30222-2-22-2-2-2-22-2-222222i2i−2i−2i-2000000002i−2i0000000000000000-2-222−2i−2i2i2i000000000000
χ31222-2-22-2-2-2-22-2-22222−2i−2i2i2i-200000000−2i2i000000000000000022-2-2−2i−2i2i2i000000000000
χ32222-2-22-2-2-2-22-2-22222−2i−2i2i2i-200000000−2i2i0000000000000000-2-2222i2i−2i−2i000000000000
χ33222-2-22-2-2-2-2-22222-2-22i2i−2i−2i222-2-2-2-222−2i2i0000000000002i2i−2i−2i00000000000000000000
χ34222-2-22-2-2-2-2-22222-2-22i2i−2i−2i2-2-22222-2-2−2i2i000000000000−2i−2i2i2i00000000000000000000
χ35222-2-22-2-2-2-2-22222-2-2−2i−2i2i2i222-2-2-2-2222i−2i000000000000−2i−2i2i2i00000000000000000000
χ36222-2-22-2-2-2-2-22222-2-2−2i−2i2i2i2-2-22222-2-22i−2i0000000000002i2i−2i−2i00000000000000000000
χ3722-22-2-22-22-20002-2002-22-20i2−i2i2−i2i2−i2i2−i2002-20000002-200i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000000000
χ3822-22-2-22-22-20002-2002-22-20i2−i2i2−i2i2−i2i2−i200-22000000-2200i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2000000000000
χ3922-22-2-22-22-20002-2002-22-20−i2i2−i2i2−i2i2−i2i2002-20000002-200−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000000000
χ4022-22-2-22-22-20002-2002-22-20−i2i2−i2i2−i2i2−i2i200-22000000-2200−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2000000000000
χ4122-22-2-22-22-20002-200-22-220i2−i2i2−i2i2−i2i2−i2002-2000000-2200−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2000000000000
χ4222-22-2-22-22-20002-200-22-220i2−i2i2−i2i2−i2i2−i200-220000002-200−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2000000000000
χ4322-22-2-22-22-20002-200-22-220−i2i2−i2i2−i2i2−i2i2002-2000000-2200i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2000000000000
χ4422-22-2-22-22-20002-200-22-220−i2i2−i2i2−i2i2−i2i200-220000002-200i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2000000000000
χ4522-2-22-2-22-220002-2002i−2i−2i2i0i2−i2−i2i2−i2i2i2−i20000002-200002i−2i−222−2i2−i2−i2i2−222−2000000000000
χ4622-2-22-2-22-220002-2002i−2i−2i2i0i2−i2−i2i2−i2i2i2−i2000000-220000−2i2i−222−2−i2i2i2−i22−2−22000000000000
χ4722-2-22-2-22-220002-2002i−2i−2i2i0−i2i2i2−i2i2−i2−i2i20000002-200002i−2i2−2−22−i2i2i2−i22−2−22000000000000
χ4822-2-22-2-22-220002-2002i−2i−2i2i0−i2i2i2−i2i2−i2−i2i2000000-220000−2i2i2−2−22i2−i2−i2i2−222−2000000000000
χ4922-2-22-2-22-220002-200−2i2i2i−2i0i2−i2−i2i2−i2i2i2−i20000002-20000−2i2i2−2−22i2−i2−i2i22−2−22000000000000
χ5022-2-22-2-22-220002-200−2i2i2i−2i0i2−i2−i2i2−i2i2i2−i2000000-2200002i−2i2−2−22−i2i2i2−i2−222−2000000000000
χ5122-2-22-2-22-220002-200−2i2i2i−2i0−i2i2i2−i2i2−i2−i2i20000002-20000−2i2i−222−2−i2i2i2−i2−222−2000000000000
χ5222-2-22-2-22-220002-200−2i2i2i−2i0−i2i2i2−i2i2−i2−i2i2000000-2200002i−2i−222−2i2−i2−i2i22−2−22000000000000
χ5344444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000000
χ54444-4-44-4-4444-4-4-4-44-4000040000000000000000000000000000000000000000000000
χ5544-44-4-44-4-44000-4400000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000000000000000
χ5644-44-4-44-4-44000-440000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000000000000000
χ5744-4-44-4-444-4000-4400000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000000
χ5844-4-44-4-444-4000-440000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000000
χ594-4-44-44-440044-400-400000000000000000000004i−4i0000000000000000000000000000
χ604-4-44-44-440044-400-40000000000000000000000−4i4i0000000000000000000000000000
χ614-4-44-44-4400-4-4400400000000000000000000000000000000000000000000000022−2200
χ624-4-44-44-4400-4-44004000000000000000000000000000000000000000000000000−222200
χ634-4-4-4444-4004-4400-400000000000000000000000000000000000000000000002i2−2i20000
χ644-4-4-4444-4004-4400-40000000000000000000000000000000000000000000000−2i22i20000
χ654-4-4-4444-400-44-40040000000000000000004-400000000000000000000000000000000
χ664-4-4-4444-400-44-4004000000000000000000-4400000000000000000000000000000000
χ678-8888-8-8-8000000000000000000000000000000000000000000000000000000000000
χ688-88-8-8-888000000000000000000000000000000000000000000000000000000000000

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