Finite Group Databasebeta

← Group #72293129

Character table — Group #72293129

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size111122222244448888888888888888888816161616161616161616161616161616161616161616161616161616323232323232323232323232323232323232323232323232323232326464646464646464
order12222244442244222244444444444444442222222222224444444444448888444444444444448888888888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ51111111111111111111111-1-1-1-11111-1-1-1-111-111111111-1-1-1-1-11111-111-1-1-1-1-111-1-111iiii−i−i−i−i-1-1-1-1-1-1iiii−i−i−i−iii−i−iii−i−i
χ61111111111111111111111-1-1-1-11111-1-1-1-111-111111111-1-1-1-1-11111-111-1-1-1-1-111-1-111−i−i−i−iiiii-1-1-1-1-1-1−i−i−i−iiiii−i−iii−i−iii
χ71111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-11111-1-1-1-1-1-1iiii−i−i−i−i111111−i−i−i−iiiiiii−i−i−i−iii
χ81111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-11111-1-1-1-1-1-1−i−i−i−iiiii111111iiii−i−i−i−i−i−iiiii−i−i
χ911111111111111-1-1-1-11111111111111111-1-111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ1011111111111111-1-1-1-11111111111111111-1-111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ1111111111111111-1-1-1-11111111111111111-1-11-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ1211111111111111-1-1-1-11111111111111111-1-11-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ1311111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-11111-1-1-1-1-11111-1-1-1-1-111-1-1-1-1-1-1-11111iiii−i−i−i−i-1-11111iiii−i−i−i−i−i−iii−i−iii
χ1411111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-11111-1-1-1-1-11111-1-1-1-1-111-1-1-1-1-1-1-11111−i−i−i−iiiii-1-11111−i−i−i−iiiiiii−i−iii−i−i
χ1511111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-11111-11111-1-1-1-1-111-111111111-1-1iiii−i−i−i−i11-1-1-1-1−i−i−i−iiiii−i−iiiii−i−i
χ1611111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-11111-11111-1-1-1-1-111-111111111-1-1−i−i−i−iiiii11-1-1-1-1iiii−i−i−i−iii−i−i−i−iii
χ17111111-1-1-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-1111-1-111-1-1-111-1-111-1-111-1-111-1-11-11-11-1ii−i−iii−i−i1-111-1-1ii−i−iii−i−ii−ii−ii−ii−i
χ18111111-1-1-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-1111-1-111-1-1-111-1-111-1-111-1-111-1-11-11-11-1−i−iii−i−iii1-111-1-1−i−iii−i−iii−ii−ii−ii−ii
χ19111111-1-1-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-11-1-111-1-111-111-1-111-1-111-1-1-1-111-111-1-11ii−i−iii−i−i-11-1-111−i−iii−i−iiii−ii−i−ii−ii
χ20111111-1-1-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-11-1-111-1-111-111-1-111-1-111-1-1-1-111-111-1-11−i−iii−i−iii-11-1-111ii−i−iii−i−i−ii−iii−ii−i
χ21111111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-11111-1-1-111-1-111-1-11-1-11111-1-1-11-11-1-1111-1-111-111-1-1-1-111-11-1-11111-1-1-1-1111-1-111-1-11
χ22111111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-11111-1-1-111-1-111-1-11-1-11111-1-1-11-11-1-1111-1-111-1-1-11111-1-1-11-1-111-1-11111-1-1-111-1-111-1
χ23111111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-11111-1-1-1-1-111-1-1111-1-11111-1-1-11-1111-1-1-11-11-1111-1-1-1-1111-111-1-1-1-11111-1-11-1-11-111-1
χ24111111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-11111-1-1-1-1-111-1-1111-1-11111-1-1-11-1111-1-1-11-11-11-1-11111-1-11-111-1-111-1-1-1-111-111-11-1-11
χ25111111-1-1-1-1-1-111-1-1-1-111-1-1111111-1-1-1-1-1-111111-1-1-1-111-1-1-111-1-11111-1-111-1-1-11-111-1ii−i−iii−i−i1-1-1-111ii−i−iii−i−i−ii−ii−ii−ii
χ26111111-1-1-1-1-1-111-1-1-1-111-1-1111111-1-1-1-1-1-111111-1-1-1-111-1-1-111-1-11111-1-111-1-1-11-111-1−i−iii−i−iii1-1-1-111−i−iii−i−iiii−ii−ii−ii−i
χ27111111-1-1-1-1-1-111-1-1-1-111-1-1111111-1-1-1-1-1-1111-1-11111-1-1-1-1-111-1-11111-1-1-1-1111-1-11-11ii−i−iii−i−i-1111-1-1−i−iii−i−iii−ii−iii−ii−i
χ28111111-1-1-1-1-1-111-1-1-1-111-1-1111111-1-1-1-1-1-1111-1-11111-1-1-1-1-111-1-11111-1-1-1-1111-1-11-11−i−iii−i−iii-1111-1-1ii−i−iii−i−ii−ii−i−ii−ii
χ29111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-111-1-1111111-111-1-1-1-111111-1-1-1-111-11-11-1-111-111-11-111-1-1-1-111-1111-1-111-1-1-1-111-111-1-111-1
χ30111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-111-1-1111111-111-1-1-1-111111-1-1-1-111-11-11-1-111-111-11-1-1-11111-1-1-1111-1-1-1-11111-1-11-1-111-1-11
χ31111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-111-1-1111111-1-1-11111-1-1111-1-1-1-111-11-1111-1-11-11-1-1111-1-1-1-1111-1-1-111-1-11111-1-1-111-11-1-11
χ32111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-111-1-1111111-1-1-11111-1-1111-1-1-1-111-11-1111-1-11-11-1-11-1-11111-1-11-1-1-11111-1-1-1-1111-1-11-111-1
χ33222222222222220000-2-2-2-222222222222200-222220000-200000000-2-2-2-222220000-2-200000000-2-200000000000000000000
χ34222222222222220000-2-2-2-222222222222200-2-2-2-2-20000-200000000-2-2-2-2-2-2-2-2000022000000002200000000000000000000
χ35222222222222220000-2-2-2-222-2-2-2-2-2-222-2-200200002222-200000000-22220000-2-2000000000000002-22-20000000000000000
χ36222222222222220000-2-2-2-222-2-2-2-2-2-222-2-20020000-2-2-2-2-200000000-222200002200000000000000-22-220000000000000000
χ37222222222222220000-2-2-2-2-2-222-2-2-2-2-2-22200-200002222200000000222-20000-2-200000000000000-22-220000000000000000
χ38222222222222220000-2-2-2-2-2-222-2-2-2-2-2-22200-20000-2-2-2-2200000000222-2000022000000000000002-22-20000000000000000
χ39222222222222220000-2-2-2-2-2-2-2-22222-2-2-2-2002222200002000000002-2-22-2-2-2-20000-2-2000000002200000000000000000000
χ40222222222222220000-2-2-2-2-2-2-2-22222-2-2-2-2002-2-2-2-200002000000002-2-22222200002200000000-2-200000000000000000000
χ412222222222222222-2-2222222-2-2-2-2-2-222-2-22-2-200000000222222-22-22-2-2-2000000-2-200000000000000000000000000000000
χ422222222222222222-2-22222-2-222-2-2-2-2-2-2222-2200000000-2-2-2-2-22-22-2-2-2-220000002200000000000000000000000000000000
χ4322222222222222-2-222222222-2-2-2-2-2-222-2-2-22-2000000002-2-2-2-2-22-222-2-2-20000002200000000000000000000000000000000
χ4422222222222222-2-2222222-2-222-2-2-2-2-2-222-22200000000-22222-22-22-2-2-22000000-2-200000000000000000000000000000000
χ45222222-2-2-2-2-2-2220000-2-222222222-2-2-2-2-2-200-222-2-20000200000000-2-22222-2-20000-2200000000-2200000000000000000000
χ46222222-2-2-2-2-2-2220000-2-222222222-2-2-2-2-2-200-2-2-2220000200000000-2-222-2-22200002-2000000002-200000000000000000000
χ47222222-2-2-2-2-2-2220000-2-22222-2-2-2-222-2-222002000022-2-2200000000-22-2-20000-22000000000000002-2-220000000000000000
χ48222222-2-2-2-2-2-2220000-2-22222-2-2-2-222-2-2220020000-2-222200000000-22-2-200002-200000000000000-222-20000000000000000
χ49222222-2-2-2-2-2-2220000-2-222-2-222-2-22222-2-200-2000022-2-2-20000000022-220000-2200000000000000-222-20000000000000000
χ50222222-2-2-2-2-2-2220000-2-222-2-222-2-22222-2-200-20000-2-222-20000000022-2200002-2000000000000002-2-220000000000000000
χ51222222-2-2-2-2-2-2220000-2-222-2-2-2-222-2-2222200222-2-20000-2000000002-22-2-2-2220000-22000000002-200000000000000000000
χ52222222-2-2-2-2-2-2220000-2-222-2-2-2-222-2-22222002-2-2220000-2000000002-22-222-2-200002-200000000-2200000000000000000000
χ53222222-2-2-2-2-2-22222-2-222-2-222-2-2-2-222-2-222-22-200000000-222-2-22-2-222-222000000-2200000000000000000000000000000000
χ54222222-2-2-2-2-2-22222-2-222-2-2-2-222-2-22222-2-2-222000000002-2-2222-2-22-2-22-20000002-200000000000000000000000000000000
χ55222222-2-2-2-2-2-222-2-22222-2-222-2-2-2-222-2-2222-2-200000000-2-2-222-222-22-2220000002-200000000000000000000000000000000
χ56222222-2-2-2-2-2-222-2-22222-2-2-2-222-2-22222-2-22-2200000000222-2-2-222-2-2-22-2000000-2200000000000000000000000000000000
χ572-2-222-222-2-22-22-2000000002i−2i2i−2i2-22-22i−2i2i−2i0002-22-2000000000000000002i−2i2i−2i0000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000
χ582-2-222-222-2-22-22-2000000002i−2i2i−2i2-22-22i−2i2i−2i0002-22-2000000000000000002i−2i2i−2i000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000
χ592-2-222-222-2-22-22-2000000002i−2i2i−2i2-22-22i−2i2i−2i000-22-2200000000000000000−2i2i−2i2i0000001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000
χ602-2-222-222-2-22-22-2000000002i−2i2i−2i2-22-22i−2i2i−2i000-22-2200000000000000000−2i2i−2i2i000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000
χ612-2-222-222-2-22-22-200000000−2i2i−2i2i2-22-2−2i2i−2i2i0002-22-200000000000000000−2i2i−2i2i0000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000
χ622-2-222-222-2-22-22-200000000−2i2i−2i2i2-22-2−2i2i−2i2i0002-22-200000000000000000−2i2i−2i2i000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000
χ632-2-222-222-2-22-22-200000000−2i2i−2i2i2-22-2−2i2i−2i2i000-22-22000000000000000002i−2i2i−2i0000001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000
χ642-2-222-222-2-22-22-200000000−2i2i−2i2i2-22-2−2i2i−2i2i000-22-22000000000000000002i−2i2i−2i000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000
χ652-2-222-2-2-222-222-2000000002i−2i2i−2i2-2-22−2i2i−2i2i0002-2-22000000000000000002i−2i−2i2i0000001−i−1+i−1+i1−i−1−i1+i1+i−1−i0000001−i−1+i−1+i1−i−1−i1+i1+i−1−i00000000
χ662-2-222-2-2-222-222-2000000002i−2i2i−2i2-2-22−2i2i−2i2i0002-2-22000000000000000002i−2i−2i2i000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i00000000
χ672-2-222-2-2-222-222-2000000002i−2i2i−2i2-2-22−2i2i−2i2i000-222-200000000000000000−2i2i2i−2i0000001−i−1+i−1+i1−i−1−i1+i1+i−1−i000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i00000000
χ682-2-222-2-2-222-222-2000000002i−2i2i−2i2-2-22−2i2i−2i2i000-222-200000000000000000−2i2i2i−2i000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i0000001−i−1+i−1+i1−i−1−i1+i1+i−1−i00000000
χ692-2-222-2-2-222-222-200000000−2i2i−2i2i2-2-222i−2i2i−2i0002-2-2200000000000000000−2i2i2i−2i0000001+i−1−i−1−i1+i−1+i1−i1−i−1+i0000001+i−1−i−1−i1+i−1+i1−i1−i−1+i00000000
χ702-2-222-2-2-222-222-200000000−2i2i−2i2i2-2-222i−2i2i−2i0002-2-2200000000000000000−2i2i2i−2i000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i00000000
χ712-2-222-2-2-222-222-200000000−2i2i−2i2i2-2-222i−2i2i−2i000-222-2000000000000000002i−2i−2i2i0000001+i−1−i−1−i1+i−1+i1−i1−i−1+i000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i00000000
χ722-2-222-2-2-222-222-200000000−2i2i−2i2i2-2-222i−2i2i−2i000-222-2000000000000000002i−2i−2i2i000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i0000001+i−1−i−1−i1+i−1+i1−i1−i−1+i00000000
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χ764444444444-4-4-4-4-4-400-44-44000000000000400000000000000040-4000000000000000000000000000000000000000000000
χ77444444-4-4-4-444-4-400444-4-4400000000000004000000000000000-40-400000000000000000000000000000000000000000000
χ78444444-4-4-4-444-4-400-4-44-4-440000000000000-400000000000000040400000000000000000000000000000000000000000000
χ79444444-4-4-4-444-4-44400-444-40000000000004000000000000000-40-4000000000000000000000000000000000000000000000
χ80444444-4-4-4-444-4-4-4-400-444-4000000000000-4000000000000000404000000000000000000000000000000000000000000000
χ814-4-444-444-4-44-44-4000000004i−4i−4i4i-44-444i−4i−4i4i0000000000000000000000000000000000000000000000000000000000000000
χ824-4-444-444-4-44-44-400000000−4i4i4i−4i-44-44−4i4i4i−4i0000000000000000000000000000000000000000000000000000000000000000
χ834-4-444-4-4-444-444-4000000004i−4i−4i4i-444-4−4i4i4i−4i0000000000000000000000000000000000000000000000000000000000000000
χ844-4-444-4-4-444-444-400000000−4i4i4i−4i-444-44i−4i−4i4i0000000000000000000000000000000000000000000000000000000000000000
χ858888-8-88-88-80000000000000000000000000000000000004-44-4000000000000000000000000000000000000000000000000
χ868888-8-88-88-8000000000000000000000000000000000000-44-44000000000000000000000000000000000000000000000000
χ878888-8-8-88-880000000000000000000000000000000000004-4-44000000000000000000000000000000000000000000000000
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χ898-8-888-888-8-8-88-88000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ908-8-888-8-8-8888-8-88000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ918-8-88-888-8-8800000000000000000000000000000004-44-400000000000000000000000000000000000000000000000000000
χ928-8-88-888-8-880000000000000000000000000000000-44-4400000000000000000000000000000000000000000000000000000
χ938-8-88-88-888-800000000000000000000000000000004-4-4400000000000000000000000000000000000000000000000000000
χ948-8-88-88-888-80000000000000000000000000000000-444-400000000000000000000000000000000000000000000000000000
χ951616-16-160000000000008-800000000000000000000000000000000000000000000000000000000000000000000000000000000
χ961616-16-16000000000000-8800000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9716-1616-1600000000008-80000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9816-1616-160000000000-880000000000000000000000000000000000000000000000000000000000000000000000000000000000

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