Finite Group Databasebeta

← Group #72226370

Character table — Group #72226370

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size111122222244444444444444448888888888888816161616161616161616161616161616161616161616161632323232323232323232323232323232323232323232646464646464646464646464
order12222222222222222222222222222222222244442222222244444444444444444444444444444444444444444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ911111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-111-1-111-1-111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1ii−i−iii−i−i
χ1011111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-111-1-111-1-111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1−i−iii−i−iii
χ1111111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i-1-111−i−iii−i−iii
χ1211111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii-1-111ii−i−iii−i−i
χ1311111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-11111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii-1-111ii−i−i−i−iii
χ1411111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-11111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-111−i−iiiii−i−i
χ1511111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-11111iiii−i−i−i−i−i−i−i−iiiii11-1-1−i−iiiii−i−i
χ1611111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-11111−i−i−i−iiiiiiiii−i−i−i−i11-1-1ii−i−i−i−iii
χ172222222222222222222222222222-2-2-2-2-2-2-2-2222222220000-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000000000
χ182222222222222222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2000022222222-2-2-2-2-2-2-2-20000000000000000000000000000000000
χ19222222222222222222-2-2-2-22222-2-222-2-222-2-2-2-2-2-200000000000000002-22-200000000000000000022-2-222-2-2000000000000
χ20222222222222222222-2-2-2-22222-2-222-2-222-2-2-2-2-2-200000000000000002-22-2000000000000000000-2-222-2-222000000000000
χ21222222222222222222-2-2-2-22222-2-2-2-222-2-222-2-2-2-20000000000000000-22-22000000000022-2-222-2-200000000000000000000
χ22222222222222222222-2-2-2-22222-2-2-2-222-2-222-2-2-2-20000000000000000-22-220000000000-2-222-2-22200000000000000000000
χ2322222222222222-2-2-2-22222-2-2-2-222-2-2-2-22222-2-2-2-222-2-20000-2-2-2-22222-2-22222-2-20000000000000000000000000000000000
χ2422222222222222-2-2-2-22222-2-2-2-222-2-2-2-22222-2-2-2-2-2-22200002222-2-2-2-2-2-222-2-2220000000000000000000000000000000000
χ2522222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-222222200000000000000002-2-220000000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ2622222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-222222200000000000000002-2-22000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ2722222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-222220000000000000000-222-200000000002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ2822222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-222220000000000000000-222-20000000000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ292222222222-2-2-2-222-2-2222222-2-2-2-2222222-2-222-2-20000222200000000-2-2-220000-2-222-2-20000000000000000000000000000
χ302222222222-2-2-2-222-2-2222222-2-2-2-2222222-2-222-2-20000-2-2-2-200000000-2-2-22000022-2-2220000000000000000000000000000
χ312222222222-2-2-2-222-2-2222222-2-2-2-2-2-2-2-2-2-22222-2-20000000000000000222-2000000000000000000000000002-22-200000000
χ322222222222-2-2-2-222-2-2222222-2-2-2-2-2-2-2-2-2-22222-2-20000000000000000222-200000000000000000000000000-22-2200000000
χ332222222222-2-2-2-222-2-2-2-2-2-222-2-22222-2-22222-2-2220000000000000000-22-2-200000000000000000000000000000000002-22-2
χ342222222222-2-2-2-222-2-2-2-2-2-222-2-22222-2-22222-2-2220000000000000000-22-2-20000000000000000000000000000000000-22-22
χ352222222222-2-2-2-222-2-2-2-2-2-222-2-222-2-222-2-2-2-2-2-22200000000000000002-2220000000000000000000000000000002i−2i2i−2i0000
χ362222222222-2-2-2-222-2-2-2-2-2-222-2-222-2-222-2-2-2-2-2-22200000000000000002-222000000000000000000000000000000−2i2i−2i2i0000
χ372222222222-2-2-2-2-2-2222222-2-222-2-22222-2-222-2-2220000222200000000-2-22-20000-2-2-2-2220000000000000000000000000000
χ382222222222-2-2-2-2-2-2222222-2-222-2-22222-2-222-2-2220000-2-2-2-200000000-2-22-200002222-2-20000000000000000000000000000
χ392222222222-2-2-2-2-2-2222222-2-222-2-2-2-2-2-222-2-2-2-222000000000000000022-22000000000000000000000000002-2-2200000000
χ402222222222-2-2-2-2-2-2222222-2-222-2-2-2-2-2-222-2-2-2-222000000000000000022-2200000000000000000000000000-222-200000000
χ412222222222-2-2-2-2-2-222-2-2-2-2-2-2222222-2-2-2-2-2-222-2-20000000000000000-222200000000000000000000000000000000002i−2i−2i2i
χ422222222222-2-2-2-2-2-222-2-2-2-2-2-2222222-2-2-2-2-2-222-2-20000000000000000-22220000000000000000000000000000000000−2i2i2i−2i
χ432222222222-2-2-2-2-2-222-2-2-2-2-2-22222-2-222222222-2-200000000000000002-2-2-20000000000000000000000000000002-2-220000
χ442222222222-2-2-2-2-2-222-2-2-2-2-2-22222-2-222222222-2-200000000000000002-2-2-2000000000000000000000000000000-222-20000
χ4544444-4-44-4-40000004-40000004-400004-4004-400002-22-2000022-2-222-2-200002-22-20000000000000000000000000000000000
χ4644444-4-44-4-40000004-40000004-400004-4004-40000-22-220000-2-222-2-2220000-22-220000000000000000000000000000000000
χ4744444-4-44-4-40000004-40000004-40000-4400-4400002-22-20000-2-222-2-22200002-22-20000000000000000000000000000000000
χ4844444-4-44-4-40000004-40000004-40000-4400-440000-22-22000022-2-222-2-20000-22-220000000000000000000000000000000000
χ4944444-4-44-4-4000000-44000000-4400004-400-4400002-2-22000022-2-2-2-22200002-2-220000000000000000000000000000000000
χ5044444-4-44-4-4000000-44000000-4400004-400-440000-222-20000-2-22222-2-20000-222-20000000000000000000000000000000000
χ5144444-4-44-4-4000000-44000000-440000-44004-400002-2-220000-2-22222-2-200002-2-220000000000000000000000000000000000
χ5244444-4-44-4-4000000-44000000-440000-44004-40000-222-2000022-2-2-2-2220000-222-20000000000000000000000000000000000
χ534444-44-4-44-400004-40000004-400004-4004-40000002-22-200002-22-22-22-20000-22-220000000000000000000000000000000000
χ544444-44-4-44-400004-40000004-400004-4004-4000000-22-220000-22-22-22-2200002-22-20000000000000000000000000000000000
χ554444-44-4-44-400004-40000004-40000-4400-440000002-22-20000-22-22-22-220000-22-220000000000000000000000000000000000
χ564444-44-4-44-400004-40000004-40000-4400-44000000-22-2200002-22-22-22-200002-22-20000000000000000000000000000000000
χ574444-44-4-44-40000-44000000-4400004-400-440000002-2-2200002-22-2-22-220000-222-20000000000000000000000000000000000
χ584444-44-4-44-40000-44000000-4400004-400-44000000-222-20000-22-222-22-200002-2-220000000000000000000000000000000000
χ594444-44-4-44-40000-44000000-440000-44004-40000002-2-220000-22-222-22-20000-222-20000000000000000000000000000000000
χ604444-44-4-44-40000-44000000-440000-44004-4000000-222-200002-22-2-22-2200002-2-220000000000000000000000000000000000
χ614444-4-44-4-4444-4-4000044-4-400004-40000000000000000000000004-4-44000000000000000000000000000000000000000000
χ624444-4-44-4-4444-4-4000044-4-400004-4000000000000000000000000-444-4000000000000000000000000000000000000000000
χ634444-4-44-4-4444-4-40000-4-4440000-44000000000000000000004-4-440000000000000000000000000000000000000000000000
χ644444-4-44-4-4444-4-40000-4-4440000-4400000000000000000000-444-40000000000000000000000000000000000000000000000
χ654444-4-44-4-44-4-444000044-4-40000-440000000000000044000000000000000000-4-40000000000000000000000000000000000
χ664444-4-44-4-44-4-444000044-4-40000-4400000000000000-4-4000000000000000000440000000000000000000000000000000000
χ674444-4-44-4-44-4-4440000-4-44400004-400000000000044000000000000000000-4-4000000000000000000000000000000000000
χ684444-4-44-4-44-4-4440000-4-44400004-4000000000000-4-400000000000000000044000000000000000000000000000000000000
χ694-4-444-44-44-4000044004-44-4-4-40000000000004-400000000000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i000000000000
χ704-4-444-44-44-4000044004-44-4-4-40000000000004-40000000000000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i000000000000
χ714-4-444-44-44-400004400-44-44-4-4000000000000-4400000000000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i000000000000
χ724-4-444-44-44-400004400-44-44-4-4000000000000-440000000000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i000000000000
χ734-4-444-44-44-40000-4-4004-44-444000000000000-4400000000000000000000000000000000000000002-22-2-22-22000000000000
χ744-4-444-44-44-40000-4-4004-44-444000000000000-440000000000000000000000000000000000000000-22-222-22-2000000000000
χ754-4-444-44-44-40000-4-400-44-44440000000000004-400000000000000000000000000000000000000002-2-22-222-2000000000000
χ764-4-444-44-44-40000-4-400-44-44440000000000004-40000000000000000000000000000000000000000-222-22-2-22000000000000
χ774-4-44-4444-4-4000000444-4-4400-4-40000000000004-40000000000000000000000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000
χ784-4-44-4444-4-4000000444-4-4400-4-40000000000004-4000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ794-4-44-4444-4-400000044-444-400-4-4000000000000-440000000000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000000000000000
χ804-4-44-4444-4-400000044-444-400-4-4000000000000-44000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000000000
χ814-4-44-4444-4-4000000-4-44-4-440044000000000000-440000000000000000000000000000002-22-2-22-2200000000000000000000
χ824-4-44-4444-4-4000000-4-44-4-440044000000000000-44000000000000000000000000000000-22-222-22-200000000000000000000
χ834-4-44-4444-4-4000000-4-4-444-400440000000000004-40000000000000000000000000000002-2-22-222-200000000000000000000
χ844-4-44-4444-4-4000000-4-4-444-400440000000000004-4000000000000000000000000000000-222-22-2-2200000000000000000000
χ854-4-44-4-4-44444-44-44-44-40000-44-4400000000000000000022-2-200000000000000002-22-22-20000000000000000000000000000
χ864-4-44-4-4-44444-44-44-44-40000-44-44000000000000000000-2-2220000000000000000-22-22-220000000000000000000000000000
χ874-4-44-4-4-44444-44-4-44-4400004-44-400000000000000000022-2-200000000000000002-2-22-220000000000000000000000000000
χ884-4-44-4-4-44444-44-4-44-4400004-44-4000000000000000000-2-2220000000000000000-222-22-20000000000000000000000000000
χ894-4-44-4-4-4444-44-444-4-440000-444-400000000000000000022-2-20000000000000000-222-2-220000000000000000000000000000
χ904-4-44-4-4-4444-44-444-4-440000-444-4000000000000000000-2-22200000000000000002-2-222-20000000000000000000000000000
χ914-4-44-4-4-4444-44-44-444-400004-4-4400000000000000000022-2-20000000000000000-22-222-20000000000000000000000000000
χ924-4-44-4-4-4444-44-44-444-400004-4-44000000000000000000-2-22200000000000000002-22-2-220000000000000000000000000000
χ938-8-8888-8-8-888-8-88000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ948-8-8888-8-8-88-888-8000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ951616-16-1600000000000000000000000000000000000000004-44-400000000000000000000000000000000000000000000000000
χ961616-16-160000000000000000000000000000000000000000-44-4400000000000000000000000000000000000000000000000000
χ9716-1616-1600000000000000000000000000000000000000004-4-4400000000000000000000000000000000000000000000000000
χ9816-1616-160000000000000000000000000000000000000000-444-400000000000000000000000000000000000000000000000000

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