Finite Group Databasebeta

← Group #72265907

Character table — Group #72265907

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111122222244444444444488888888888816161616161616161616323232323232323232323232323232323232323232323232323232323232646464646464646464646464
order12222222222222222222222222222222442222244444444444444444444444444444444444444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ511111111111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111111-1-1-1-111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ811111111111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1
χ9111111111111-1-1-1-1-111-1-1-111111111-1-1-1-1-1111111-1-1-111-1-1-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i11-1-1ii−i−iii−i−i
χ10111111111111-1-1-1-1-111-1-1-111111111-1-1-1-1-1111111-1-1-111-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii11-1-1−i−iii−i−iii
χ11111111111111-1-1-1-1-111-1-1-111111111-1-1-1-1-1111111-1-1-111-1-1-1-1-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iii-1-111ii−i−i−i−iii
χ12111111111111-1-1-1-1-111-1-1-111111111-1-1-1-1-1111111-1-1-111-1-1-1-1-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i-1-111−i−iiiii−i−i
χ13111111111111-1-1-1-1-111-1-1-111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-111111111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i-1-111−i−iii−i−iii
χ14111111111111-1-1-1-1-111-1-1-111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-111111111-1-1-1-1−i−iii−i−iii−i−iii−i−iii-1-111ii−i−iii−i−i
χ15111111111111-1-1-1-1-111-1-1-111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-11111-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iii11-1-1−i−iiiii−i−i
χ16111111111111-1-1-1-1-111-1-1-111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-11111-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i11-1-1ii−i−i−i−iii
χ17222222222222222222222222-2-2-2-222-2-2-2-2-20000-2-222-200000022-2-222-2-20000000000000000000000000000
χ18222222222222222222222222-2-2-2-222-2-2-2-2-20000-2-222-2000000-2-222-2-2220000000000000000000000000000
χ192222222222222222222222-2-222-2-2-2-222-2-2-200002-2-2-220000000000000022220000-2-2-2-20000000000000000
χ202222222222222222222222-2-222-2-2-2-222-2-2-200002-2-2-2200000000000000-2-2-2-2000022220000000000000000
χ212222222222222222222222-2-2-2-222-2-2-2-22220000-22-2-2-200000000000000000022220000-2-2-2-2000000000000
χ222222222222222222222222-2-2-2-222-2-2-2-22220000-22-2-2-2000000000000000000-2-2-2-200002222000000000000
χ23222222222222-2-2-2-2-222-2-2-222-2-2-2-222222220000-2-2-2-2200000022-2-2-2-2220000000000000000000000000000
χ24222222222222-2-2-2-2-222-2-2-222-2-2-2-222222220000-2-2-2-22000000-2-22222-2-20000000000000000000000000000
χ25222222222222-2-2-2-2-222-2-2-2-2-222-2-2-2-2-2-222200002-222-2000000000000002i2i−2i−2i0000−2i−2i2i2i0000000000000000
χ26222222222222-2-2-2-2-222-2-2-2-2-222-2-2-2-2-2-222200002-222-200000000000000−2i−2i2i2i00002i2i−2i−2i0000000000000000
χ27222222222222-2-2-2-2-222-2-2-2-2-2-2-222-2-222-2-2-20000-222220000000000000000002i2i−2i−2i0000−2i−2i2i2i000000000000
χ28222222222222-2-2-2-2-222-2-2-2-2-2-2-222-2-222-2-2-20000-22222000000000000000000−2i−2i2i2i00002i2i−2i−2i000000000000
χ292222222222-2-22222-2-2-2-2-2-2222222-2-2-2-2-2-222222-2-22-22-2-222-2-2000000000000000000000000000000000000
χ302222222222-2-22222-2-2-2-2-2-2222222-2-2-2-2-2-22-2-2-2-2-2-22-2222-2-222000000000000000000000000000000000000
χ312222222222-2-22222-2-2-2-2-2-222-2-2-2-2-2-22222-20000222-2-20000000000000000000000000000002i−2i2i−2i00000000
χ322222222222-2-22222-2-2-2-2-2-222-2-2-2-2-2-22222-20000222-2-2000000000000000000000000000000−2i2i−2i2i00000000
χ332222222222-2-22222-2-2-2-2-2-2-2-222-2-222-2-222-20000-22-22200000000000000000000000000000000002i−2i2i−2i0000
χ342222222222-2-22222-2-2-2-2-2-2-2-222-2-222-2-222-20000-22-2220000000000000000000000000000000000−2i2i−2i2i0000
χ352222222222-2-22222-2-2-2-2-2-2-2-2-2-2222222-2-2200002-2-22-2000000000000000000000000000000000000002i−2i2i−2i
χ362222222222-2-22222-2-2-2-2-2-2-2-2-2-2222222-2-2200002-2-22-200000000000000000000000000000000000000−2i2i−2i2i
χ372222222222-2-2-2-2-2-22-2-2222222222-2-22222-22222-2-2-22-2-2-2-2-222000000000000000000000000000000000000
χ382222222222-2-2-2-2-2-22-2-2222222222-2-22222-2-2-2-2-2-2-2-22-22222-2-2000000000000000000000000000000000000
χ392222222222-2-2-2-2-2-22-2-222222-2-2-2-2-2-2-2-2-2-22000022-2220000000000000000000000000000002i−2i−2i2i00000000
χ402222222222-2-2-2-2-2-22-2-222222-2-2-2-2-2-2-2-2-2-22000022-222000000000000000000000000000000−2i2i2i−2i00000000
χ412222222222-2-2-2-2-2-22-2-2222-2-222-2-22222-2-220000-222-2-200000000000000000000000000000000002-2-220000
χ422222222222-2-2-2-2-2-22-2-2222-2-222-2-22222-2-220000-222-2-20000000000000000000000000000000000-222-20000
χ432222222222-2-2-2-2-2-22-2-2222-2-2-2-22222-2-222-200002-22-22000000000000000000000000000000000000002-2-22
χ442222222222-2-2-2-2-2-22-2-2222-2-2-2-22222-2-222-200002-22-2200000000000000000000000000000000000000-222-2
χ4544444-4-44-4-40000004004-4-4004-400004-40000000000000000000000000000002i−2i2i−2i00002i−2i2i−2i000000000000
χ4644444-4-44-4-40000004004-4-4004-400004-4000000000000000000000000000000−2i2i−2i2i0000−2i2i−2i2i000000000000
χ4744444-4-44-4-40000004004-4-400-440000-440000000000000000000000000000002i−2i2i−2i0000−2i2i−2i2i000000000000
χ4844444-4-44-4-40000004004-4-400-440000-44000000000000000000000000000000−2i2i−2i2i00002i−2i2i−2i000000000000
χ4944444-4-44-4-4000000-400-444004-40000-440000000000000000000000000000002-2-2200002-2-22000000000000
χ5044444-4-44-4-4000000-400-444004-40000-44000000000000000000000000000000-222-20000-222-2000000000000
χ5144444-4-44-4-4000000-400-44400-4400004-40000000000000000000000000000002-2-220000-222-2000000000000
χ5244444-4-44-4-4000000-400-44400-4400004-4000000000000000000000000000000-222-200002-2-22000000000000
χ534-4-4444-4-44-44400000-4-40004-400004-4000000000000000000000000004i−4i0000000000000000000000000000
χ544-4-4444-4-44-44400000-4-40004-400004-400000000000000000000000000−4i4i0000000000000000000000000000
χ554-4-4444-4-44-44400000-4-4000-440000-4400000000000000000000004i−4i00000000000000000000000000000000
χ564-4-4444-4-44-44400000-4-4000-440000-440000000000000000000000−4i4i00000000000000000000000000000000
χ574-4-4444-4-44-4-4-400000440004-40000-440000000000000000000000004-4000000000000000000000000000000
χ584-4-4444-4-44-4-4-400000440004-40000-44000000000000000000000000-44000000000000000000000000000000
χ594-4-4444-4-44-4-4-40000044000-4400004-4000000000000000000004-40000000000000000000000000000000000
χ604-4-4444-4-44-4-4-40000044000-4400004-400000000000000000000-440000000000000000000000000000000000
χ614-4-44-4444-4-4000000400-44-400004-400004-40000000000000000000000002i−2i2i−2i00002i−2i2i−2i0000000000000000
χ624-4-44-4444-4-4000000400-44-400004-400004-4000000000000000000000000−2i2i−2i2i0000−2i2i−2i2i0000000000000000
χ634-4-44-4444-4-4000000400-44-40000-440000-440000000000000000000000002i−2i2i−2i0000−2i2i−2i2i0000000000000000
χ644-4-44-4444-4-4000000400-44-40000-440000-44000000000000000000000000−2i2i−2i2i00002i−2i2i−2i0000000000000000
χ654-4-44-4444-4-4000000-4004-4400004-40000-440000000000000000000000002-2-2200002-2-220000000000000000
χ664-4-44-4444-4-4000000-4004-4400004-40000-44000000000000000000000000-222-20000-222-20000000000000000
χ674-4-44-4444-4-4000000-4004-440000-4400004-40000000000000000000000002-2-220000-222-20000000000000000
χ684-4-44-4444-4-4000000-4004-440000-4400004-4000000000000000000000000-222-200002-2-220000000000000000
χ694-4-44-4-4-44444-444-4-444-4-4-44000000000000022-2-2000002-22-22-2000000000000000000000000000000000000
χ704-4-44-4-4-44444-444-4-444-4-4-440000000000000-2-22200000-22-22-22000000000000000000000000000000000000
χ714-4-44-4-4-44444-4-4-444-44-444-4000000000000022-2-2000002-2-22-22000000000000000000000000000000000000
χ724-4-44-4-4-44444-4-4-444-44-444-40000000000000-2-22200000-222-22-2000000000000000000000000000000000000
χ734-4-44-4-4-4444-4444-4-4-4-4444-4000000000000022-2-200000-222-2-22000000000000000000000000000000000000
χ744-4-44-4-4-4444-4444-4-4-4-4444-40000000000000-2-222000002-2-222-2000000000000000000000000000000000000
χ754-4-44-4-4-4444-44-4-4444-44-4-44000000000000022-2-200000-22-222-2000000000000000000000000000000000000
χ764-4-44-4-4-4444-44-4-4444-44-4-440000000000000-2-222000002-22-2-22000000000000000000000000000000000000
χ778888-88-8-8-88008-88-80000000000000000000000000000000000000000000000000000000000000000000000
χ788888-88-8-8-8800-88-880000000000000000000000000000000000000000000000000000000000000000000000
χ798888-8-88-88-88-800000-880000000000000000000000000000000000000000000000000000000000000000000
χ808888-8-88-88-8-88000008-80000000000000000000000000000000000000000000000000000000000000000000
χ818-8-888-88-8-88008-8-880000000000000000000000000000000000000000000000000000000000000000000000
χ828-8-888-88-8-8800-888-80000000000000000000000000000000000000000000000000000000000000000000000
χ831616-16-1600000000000000000000000000000004-44-400000000000000000000000000000000000000000000000
χ841616-16-160000000000000000000000000000000-44-4400000000000000000000000000000000000000000000000
χ8516-1616-1600000000000000000000000000000004-4-4400000000000000000000000000000000000000000000000
χ8616-1616-160000000000000000000000000000000-444-400000000000000000000000000000000000000000000000

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