Finite Group Databasebeta

← Group #72265787

Character table — Group #72265787

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size111122222222444444444444444888888888888888816161616161616161616161616161616161616323232323232323232323232323232323232323232323232646464646464646464646464
order12222222222222222222222222222222222224444442222224444444444444244444444444444444444444444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ5111111111111111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ7111111111111111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1
χ8111111111111111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ91111111111111111111111-1-11-1-11111-1-1-1-1-1-11111-1-1-1-11111-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iii−i−iii−i−iii−i−i
χ101111111111111111111111-1-11-1-11111-1-1-1-1-1-11111-1-1-1-11111-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−iii−i−iii−i−iii
χ111111111111111111111111-1-11-1-11111-1-1-1-1-1-11111-1-1-1-11111-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111iiii−i−i−i−i−i−iii−i−iiiii−i−i
χ121111111111111111111111-1-11-1-11111-1-1-1-1-1-11111-1-1-1-11111-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111−i−i−i−iiiiiii−i−iii−i−i−i−iii
χ131111111111111111111111-1-11-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111iiii−i−i−i−iii−i−i−i−iii−i−iii
χ141111111111111111111111-1-11-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111−i−i−i−iiiii−i−iiiii−i−iii−i−i
χ151111111111111111111111-1-11-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−iiiii−i−i−i−iii
χ161111111111111111111111-1-11-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiii−i−i−i−iiiii−i−i
χ17222222222222222222222222222-2-2-2-22222-2-2-2-2-2-2-2-22-20000-20000000000002-2-2222-2-20000000000000000000000000000
χ18222222222222222222222222222-2-2-2-22222-2-2-2-2-2-2-2-22-20000-2000000000000-222-2-2-2220000000000000000000000000000
χ192222222222222222222222-2-22-2-2-2-2-2-2-2-2-2-222-2-2-2-222-22000020000000000002-2-22-2-2220000000000000000000000000000
χ202222222222222222222222-2-22-2-2-2-2-2-2-2-2-2-222-2-2-2-222-2200002000000000000-222-222-2-20000000000000000000000000000
χ2122222222222222-2-2-2-2-2-2-2-222222222222-2-222-2-2-2-2-2-2-220000-20000000000000000000022-2-222-2-200000000000000000000
χ2222222222222222-2-2-2-2-2-2-2-222222222222-2-222-2-2-2-2-2-2-220000-200000000000000000000-2-222-2-22200000000000000000000
χ2322222222222222-2-2-2-2-2-2-2-222222-2-2-2-222-2-2-2-2222222-2-222-2-2222-2-22222-2-2-2-2000000000000000000000000000000000000
χ2422222222222222-2-2-2-2-2-2-2-222222-2-2-2-222-2-2-2-2222222-2-2-2-2222-2-222-2-2-2-22222000000000000000000000000000000000000
χ2522222222222222-2-2-2-2-2-2-2-2-2-22-2-22222-2-222-2-2-2-2-2-2222-2000020000000000000000000022-2-2-2-22200000000000000000000
χ2622222222222222-2-2-2-2-2-2-2-2-2-22-2-22222-2-222-2-2-2-2-2-2222-20000200000000000000000000-2-22222-2-200000000000000000000
χ2722222222222222-2-2-2-2-2-2-2-2-2-22-2-2-2-2-2-2-2-222222222-2-22222-2-2-222-2-2-2-2-2-22222000000000000000000000000000000000000
χ2822222222222222-2-2-2-2-2-2-2-2-2-22-2-2-2-2-2-2-2-222222222-2-222-2-222-2-2-2222222-2-2-2-2000000000000000000000000000000000000
χ29222222222-2-22-2-22222-2-2-2-222-22222-2-2-2-2222222-2-2-2-2-2-2000020000000000000000000000000000000000002-22-200000000
χ30222222222-2-22-2-22222-2-2-2-222-22222-2-2-2-2222222-2-2-2-2-2-200002000000000000000000000000000000000000-22-2200000000
χ31222222222-2-22-2-22222-2-2-2-222-222-2-222-2-222-2-2-2-22222-220000-2000000000000000000000000000022-2-222-2-2000000000000
χ32222222222-2-22-2-22222-2-2-2-222-222-2-222-2-222-2-2-2-22222-220000-20000000000000000000000000000-2-222-2-222000000000000
χ33222222222-2-22-2-22222-2-2-2-2-2-2-2-2-222-2-222-2-2-2-222-2-222220000-20000000000000000000000000000000000002i−2i−2i2i00000000
χ34222222222-2-22-2-22222-2-2-2-2-2-2-2-2-222-2-222-2-2-2-222-2-222220000-2000000000000000000000000000000000000−2i2i2i−2i00000000
χ35222222222-2-22-2-22222-2-2-2-2-2-2-2-2-2-2-22222-2-222-2-222-2-22-20000200000000000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ36222222222-2-22-2-22222-2-2-2-2-2-2-2-2-2-2-22222-2-222-2-222-2-22-2000020000000000000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ37222222222-2-22-2-2-2-2-2-2222222-22222-2-2-2-2-2-222-2-222222-20000-2000000000000000000000000000000000000000000002-22-2
χ38222222222-2-22-2-2-2-2-2-2222222-22222-2-2-2-2-2-222-2-222222-20000-200000000000000000000000000000000000000000000-22-22
χ39222222222-2-22-2-2-2-2-2-2222222-222-2-222-2-2-2-2-2-222-2-2-2-2220000200000000000000000000000000000000000000002i−2i2i−2i0000
χ40222222222-2-22-2-2-2-2-2-2222222-222-2-222-2-2-2-2-2-222-2-2-2-222000020000000000000000000000000000000000000000−2i2i−2i2i0000
χ41222222222-2-22-2-2-2-2-2-22222-2-2-2-2-222-2-22222-2-2-2-222-2-2-2200002000000000000000000000000000000000000000000002i−2i−2i2i
χ42222222222-2-22-2-2-2-2-2-22222-2-2-2-2-222-2-22222-2-2-2-222-2-2-220000200000000000000000000000000000000000000000000−2i2i2i−2i
χ43222222222-2-22-2-2-2-2-2-22222-2-2-2-2-2-2-22222222222-2-222-2-20000-200000000000000000000000000000000000000002-2-220000
χ44222222222-2-22-2-2-2-2-2-22222-2-2-2-2-2-2-22222222222-2-222-2-20000-20000000000000000000000000000000000000000-222-20000
χ45444444-4-4-444-4-4-400000000004004-44-4000000000000000000000000000000000000000004-4000000000000000000000000
χ46444444-4-4-444-4-4-400000000004004-44-400000000000000000000000000000000000000000-44000000000000000000000000
χ47444444-4-4-444-4-4-40000000000400-44-440000000000000000000000000000000000000004-400000000000000000000000000
χ48444444-4-4-444-4-4-40000000000400-44-44000000000000000000000000000000000000000-4400000000000000000000000000
χ49444444-4-4-4-4-4-4440000000000-4004-4-4400000000000000000000000000000000000000000004i−4i0000000000000000000000
χ50444444-4-4-4-4-4-4440000000000-4004-4-440000000000000000000000000000000000000000000−4i4i0000000000000000000000
χ51444444-4-4-4-4-4-4440000000000-400-444-40000000000000000000000000000000000000000000004i−4i00000000000000000000
χ52444444-4-4-4-4-4-4440000000000-400-444-4000000000000000000000000000000000000000000000−4i4i00000000000000000000
χ534444-4-44-4-44444-40000000000-40000000000004-44-400000044000-4-400000000000000000000000000000000000000000000
χ544444-4-44-4-44444-40000000000-40000000000004-44-4000000-4-40004400000000000000000000000000000000000000000000
χ554444-4-44-4-44444-40000000000-4000000000000-44-44000044000-4-40000000000000000000000000000000000000000000000
χ564444-4-44-4-44444-40000000000-4000000000000-44-440000-4-4000440000000000000000000000000000000000000000000000
χ574444-4-44-4-4-4-44-44000000000040000000000004-4-44000000000000044-4-40000000000000000000000000000000000000000
χ584444-4-44-4-4-4-44-44000000000040000000000004-4-440000000000000-4-4440000000000000000000000000000000000000000
χ594444-4-44-4-4-4-44-4400000000004000000000000-444-40000000000000000044-4-4000000000000000000000000000000000000
χ604444-4-44-4-4-4-44-4400000000004000000000000-444-400000000000000000-4-444000000000000000000000000000000000000
χ614444-4-4-44444-4-4444-4-444-4-400-4000000000000000000000000000000000000004-4000000000000000000000000000000000
χ624444-4-4-44444-4-4444-4-444-4-400-400000000000000000000000000000000000000-44000000000000000000000000000000000
χ634444-4-4-44444-4-44-4-444-4-44400-40000000000000000000000000000000000000400-400000000000000000000000000000000
χ644444-4-4-44444-4-44-4-444-4-44400-40000000000000000000000000000000000000-400400000000000000000000000000000000
χ654444-4-4-444-4-4-44-444-4-4-4-44400400000000000000000000000000000000000000000004-40000000000000000000000000000
χ664444-4-4-444-4-4-44-444-4-4-4-4440040000000000000000000000000000000000000000000-440000000000000000000000000000
χ674444-4-4-444-4-4-44-4-4-44444-4-4004000000000000000000000000000000000000000004-4000000000000000000000000000000
χ684444-4-4-444-4-4-44-4-4-44444-4-400400000000000000000000000000000000000000000-44000000000000000000000000000000
χ694-4-444-4-44-40040000004-44-400000000000004-400004-4002-22-202-22-22-22-22-22-2000000000000000000000000000000000000
χ704-4-444-4-44-40040000004-44-400000000000004-400004-400-22-220-22-22-22-22-22-22000000000000000000000000000000000000
χ714-4-444-4-44-40040000004-44-40000000000000-440000-44002-22-202-22-2-22-22-22-22000000000000000000000000000000000000
χ724-4-444-4-44-40040000004-44-40000000000000-440000-4400-22-220-22-222-22-22-22-2000000000000000000000000000000000000
χ734-4-444-4-44-4004000000-44-4400000000000004-40000-44002-2-2202-2-22-22-222-22-2000000000000000000000000000000000000
χ744-4-444-4-44-4004000000-44-4400000000000004-40000-4400-222-20-222-22-22-2-22-22000000000000000000000000000000000000
χ754-4-444-4-44-4004000000-44-440000000000000-4400004-4002-2-2202-2-222-22-2-22-22000000000000000000000000000000000000
χ764-4-444-4-44-4004000000-44-440000000000000-4400004-400-222-20-222-2-22-222-22-2000000000000000000000000000000000000
χ774-4-44-44-4-44004004-44-400004-404-40000004-400000000002-22-20-22-222-2-222-2-22000000000000000000000000000000000000
χ784-4-44-44-4-44004004-44-400004-404-40000004-40000000000-22-2202-22-2-222-2-222-2000000000000000000000000000000000000
χ794-4-44-44-4-44004004-44-40000-440-44000000-4400000000002-22-20-22-22-222-2-222-2000000000000000000000000000000000000
χ804-4-44-44-4-44004004-44-40000-440-44000000-440000000000-22-2202-22-22-2-222-2-22000000000000000000000000000000000000
χ814-4-44-44-4-4400400-44-4400004-404-4000000-4400000000002-2-220-222-22-2-22-222-2000000000000000000000000000000000000
χ824-4-44-44-4-4400400-44-4400004-404-4000000-440000000000-222-202-2-22-222-22-2-22000000000000000000000000000000000000
χ834-4-44-44-4-4400400-44-440000-440-440000004-400000000002-2-220-222-2-222-22-2-22000000000000000000000000000000000000
χ844-4-44-44-4-4400400-44-440000-440-440000004-40000000000-222-202-2-222-2-22-222-2000000000000000000000000000000000000
χ8588-8-8000008-800000000000440-4-400004-40000000000000000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i000000000000
χ8688-8-8000008-800000000000440-4-400004-4000000000000000000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i000000000000
χ8788-8-8000008-800000000000-4-40440000-440000000000000000000000000000000000000000000002-22-2-22-22000000000000
χ8888-8-8000008-800000000000-4-40440000-44000000000000000000000000000000000000000000000-22-222-22-2000000000000
χ8988-8-800000-8800000000000440-4-40000-440000000000000000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i000000000000
χ9088-8-800000-8800000000000440-4-40000-44000000000000000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i000000000000
χ9188-8-800000-8800000000000-4-404400004-40000000000000000000000000000000000000000000002-2-22-222-2000000000000
χ9288-8-800000-8800000000000-4-404400004-4000000000000000000000000000000000000000000000-222-22-2-22000000000000
χ938-8-888-88-8800-8008-8-8800000000000000000000000000000000000000000000000000000000000000000000000000000000
χ948-8-888-88-8800-800-888-800000000000000000000000000000000000000000000000000000000000000000000000000000000
χ958-8-88-8888-800-80000008-8-880000000000000000000000000000000000000000000000000000000000000000000000000000
χ968-8-88-8888-800-8000000-888-80000000000000000000000000000000000000000000000000000000000000000000000000000
χ9716-1616-160000000000000000008-80-8800000000000000000000000000000000000000000000000000000000000000000000000
χ9816-1616-16000000000000000000-8808-800000000000000000000000000000000000000000000000000000000000000000000000

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