Finite Group Databasebeta

← Group #72262474

Character table — Group #72262474

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11222444488888888816161616161616161616161616161616161616161616161616161616161632326464646464646464646464646464128128128128
order12222222222222224422222222224444444444444444444444444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-111111-11111111111111-1-1-1-1-1-1-1-1-1ii−i−iii−i−iii−i−i
χ411111111111111111111111111-1-111111-11111111111111-1-1-1-1-1-1-1-1-1−i−iii−i−iii−i−iii
χ51111111111111111111111-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-11-11-1
χ61111111111111111111111-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-11111-11-11
χ71111111111111111111111-1-1-1-1-1-11-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−i−i−iiii−i−ii
χ81111111111111111111111-1-1-1-1-1-11-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−iiiii−i−i−iii−i
χ91111111111111-1-11-1-11-1-1-111-1-111111-1-1111-1-1-11111-1-1-1-1111-1-111-1-111111111-1-1-1-1
χ101111111111111-1-11-1-11-1-1-111-1-111111-1-1111-1-1-11111-1-1-1-1111-1-111-1-1-1-1-1-1-1-1-1-11111
χ111111111111111-1-11-1-11-1-1-111-1-1-1-1111-1-1-111-1-1-11111-1-1-1-1-1-1-111-1-111ii−i−iii−i−i−i−iii
χ121111111111111-1-11-1-11-1-1-111-1-1-1-1111-1-1-111-1-1-11111-1-1-1-1-1-1-111-1-111−i−iii−i−iiiii−i−i
χ131111111111111-1-11-1-11-1-1-1-1-111111-1-111111-1-1-1-1-1-1-11111111-1-1-1-1111111-1-1-1-1-11-11
χ141111111111111-1-11-1-11-1-1-1-1-111111-1-111111-1-1-1-1-1-1-11111111-1-1-1-111-1-1-1-111111-11-1
χ151111111111111-1-11-1-11-1-1-1-1-111-1-11-1-111-111-1-1-1-1-1-1-11111-1-1-11111-1-1ii−i−i−i−iii−iii−i
χ161111111111111-1-11-1-11-1-1-1-1-111-1-11-1-111-111-1-1-1-1-1-1-11111-1-1-11111-1-1−i−iiiii−i−ii−i−ii
χ17222222222222200200-20002-20022-22-2002-2-200022-2-200002-2-2002-200000000000000
χ18222222222222200200-20002-200-2-2-22-200-2-2-200022-2-20000-22200-2200000000000000
χ19222222222222200200-2000-220022-2-22002-2-2000-2-22200002-2-200-2200000000000000
χ20222222222222200200-2000-2200-2-2-2-2200-2-2-2000-2-2220000-222002-200000000000000
χ21222222222-2-2-2-200200-2000002-222-2002-2-222000000022-2-2-22-200002-2000000000000
χ22222222222-2-2-2-200200-2000002-2-2-2-2002-2222000000022-2-22-220000-22000000000000
χ23222222222-2-2-2-200200-200000-2222-200-22-2220000000-2-222-22-20000-22000000000000
χ24222222222-2-2-2-200200-200000-22-2-2-200-222220000000-2-2222-2200002-2000000000000
χ25222222222-2-2-2-2222-2-222-2-200002220000-2-2-222-200000000-2-222-20000000000000000
χ26222222222-2-2-2-2222-2-222-2-20000-2-2200002-2-222-20000000022-2-220000000000000000
χ27222222222-2-2-2-2-2-22222-22200002220000-2-2-2-2-2200000000-2-22-220000000000000000
χ28222222222-2-2-2-2-2-22222-2220000-2-2200002-2-2-2-220000000022-22-20000000000000000
χ294444444-4-4000000-444-40-4-40000004000000000400000000000000000000000000000
χ304444444-4-4000000-4-4-4-40440000004000000000-400000000000000000000000000000
χ314444444-4-4000044-4004400000000-40000000-4-4000000000000000000000000000000
χ324444444-4-40000-4-4-4004-400000000-4000000044000000000000000000000000000000
χ3344444-4-44444-4-400-40000000400000040000000000-4-40000000000000000000000000
χ3444444-4-44444-4-400-40000000-4000000-40000000000440000000000000000000000000
χ3544444-4-444-4-44400-400000040000004000000000-4-4000000000000000000000000000
χ3644444-4-444-4-44400-4000000-4000000-400000000044000000000000000000000000000
χ3744444-4-4-4-400000040000000004000000404-4000000000-4-4000000000000000000000
χ3844444-4-4-4-40000004000000000-4000000-404-400000000044000000000000000000000
χ3944444-4-4-4-40000004000000004000000400-440000000-4-400000000000000000000000
χ4044444-4-4-4-4000000400000000-4000000-400-4400000004400000000000000000000000
χ4144-4-44004-4004-4220220-22-24022000-40-2-20002-2-200002-22-2000000000000000000000
χ4244-4-44004-4004-4220220-22-2-40-2-200040220002-2-20000-22-22000000000000000000000
χ4344-4-44004-4004-4-2-20-2-202-2240-2-2000-4022000-2220000-22-22000000000000000000000
χ4444-4-44004-4004-4-2-20-2-202-22-402200040-2-2000-22200002-22-2000000000000000000000
χ4544-4-44004-400-44220-2-20-2-22002-200000-220002-224-4002-2-22000000000000000000000
χ4644-4-44004-400-44220-2-20-2-2200-22000002-20002-22-4400-222-2000000000000000000000
χ4744-4-44004-400-44-2-2022022-2002-200000-22000-22-2-44002-2-22000000000000000000000
χ4844-4-44004-400-44-2-2022022-200-22000002-2000-22-24-400-222-2000000000000000000000
χ4944-4-4400-444-400220220-2-2204220000-4-2-2000-22-20000-22-22000000000000000000000
χ5044-4-4400-444-400220220-2-220-4-2-20000422000-22-200002-22-2000000000000000000000
χ5144-4-4400-444-400-2-20-2-2022-204-2-20000-4220002-2200002-22-2000000000000000000000
χ5244-4-4400-444-400-2-20-2-2022-20-42200004-2-20002-220000-22-22000000000000000000000
χ5344-4-4400-44-4400220-2-20-22-2002-200000-22000-222004-4-222-2000000000000000000000
χ5444-4-4400-44-4400220-2-20-22-200-22000002-2000-22200-442-2-22000000000000000000000
χ5544-4-4400-44-4400-2-202202-22002-200000-220002-2-200-44-222-2000000000000000000000
χ5644-4-4400-44-4400-2-202202-2200-22000002-20002-2-2004-42-2-22000000000000000000000
χ57888-8-8000000000000000000000000000040000000000000-40000000000002i−2i2i−2i0000
χ58888-8-8000000000000000000000000000040000000000000-4000000000000−2i2i−2i2i0000
χ59888-8-80000000000000000000000000000-4000000000000040000000000002-2-220000
χ60888-8-80000000000000000000000000000-400000000000004000000000000-222-20000
χ6188-88-80000000000000000000004-400000000000000000000000000002i−2i2i−2i00000000
χ6288-88-80000000000000000000004-40000000000000000000000000000−2i2i−2i2i00000000
χ6388-88-8000000000000000000000-4400000000000000000000000000002-2-2200000000
χ6488-88-8000000000000000000000-440000000000000000000000000000-222-200000000
χ6516-160008-80000000008-800000000000000000000000000000000000000000000000000
χ6616-160008-8000000000-8800000000000000000000000000000000000000000000000000
χ6716-16000-880000008-800000000000000000000000000000000000000000000000000000
χ6816-16000-88000000-8800000000000000000000000000000000000000000000000000000

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