Finite Group Databasebeta

← Group #72267052

Character table — Group #72267052

Order 6144.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size11244466881212121212121212121212161624242424242424242424242424243232323232484848484848484848484848484864969696969696969696969696969696969696969696128128128128128192192192192256256256256256
order12222422882222224444422222244448888883444622224444888888644444444444444488888866661244441212122424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111-1-1111111111111111-1-1-1111-1-111111111111-1-1-1-1-1-1-11111-1-1-1-11111111-1-111-1-1-1-1-1-1-111
χ311111111111111111-1-111111-1-11111-111111111111-1-1-1-1-1-1-1-111-1-1-1-11-1-1-11-11-1-1-1-1-111-1-1-1-1-1-1-1-111111-1-1-1-111111
χ411111111111111111-1-111-1-11-1-11111-11111111-1-1-11-1-111-1-1-1-111-1-1-1-11111-11-11-1-1-1-1-1-111-1-1-1-1-1-11-1-1111111-1-1-111
χ511111111-1-1111111111111111111111-1-1-1-1-1-111-1-1111111111-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-11-1-1-1-1
χ611111111-1-111111111111-1-111111111-1-1-1-1-1-11-111111-1-11111-1-111111-111-1-1-1-1-1-1-1-11111-1-1-1-1111-1-111-1-111-111-1-1
χ711111111-1-11111111-1-111111-1-11111-1-1-1-1-1-1-111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-11-11111-1-1111111-1-111111-1-1111-1-1-1-1
χ811111111-1-11111111-1-111-1-11-1-11111-1-1-1-1-1-1-11-1111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-11-11111111-1-11111-1-11-1-11111-1-1-111-1-1
χ91111-1-111i−i111-1-1-1111-1111111-11-1-11iii−i−i−i1-1i−i11-111-11-1-1i−i11-1-11-1i−i-1-111ii−i−ii−ii−ii−ii−i1-1111-1-11-1i−i-1i−ii−i
χ101111-1-111i−i111-1-1-1111-11-1-1111-11-1-11iii−i−i−i11−ii11-1-1-1-11-1-1i−i11-1-111−ii11-1-1ii−i−i−ii−iii−ii−i1-11-1-1-1-1-11−ii1−iii−i
χ111111-1-111i−i111-1-1-11-1-1-11111-1-1-11-1-1-1iii−i−i−i1-1i−i1-11-1-11-111i−i-1-11111−ii-111-1−i−iiii−i−ii−ii−ii-11111-1-1-11−ii-1i−ii−i
χ121111-1-111i−i111-1-1-11-1-1-11-1-11-1-1-11-1-1-1iii−i−i−i11−ii1-11111-111i−i-1-1111-1i−i1-1-11−i−iii−iii−i−ii−ii-111-1-1-1-11-1i−i1−iii−i
χ131111-1-111−ii111-1-1-1111-1111111-11-1-11−i−i−iiii1-1−ii11-111-11-1-1−ii11-1-11-1−ii-1-111−i−iii−ii−ii−ii−ii1-1111-1-11-1−ii-1−ii−ii
χ141111-1-111−ii111-1-1-1111-11-1-1111-11-1-11−i−i−iiii11i−i11-1-1-1-11-1-1−ii11-1-111i−i11-1-1−i−iiii−ii−i−ii−ii1-11-1-1-1-1-11i−i1i−i−ii
χ151111-1-111−ii111-1-1-11-1-1-11111-1-1-11-1-1-1−i−i−iiii1-1−ii1-11-1-11-111−ii-1-11111i−i-111-1ii−i−i−iii−ii−ii−i-11111-1-1-11i−i-1−ii−ii
χ161111-1-111−ii111-1-1-11-1-1-11-1-11-1-1-11-1-1-1−i−i−iiii11i−i1-11111-111−ii-1-1111-1−ii1-1-11ii−i−ii−i−iii−ii−i-111-1-1-1-11-1−ii1i−i−ii
χ172222222222222222200222220022220222222-1222-100000000220000-1000202000002200000000-1-1-1-1-10000-1-1-1-1-1
χ18222222222222222220022-2-220022220222222-1-2-2-2-100000000220000-1000-20-200000-2-200000000-111-1-10000111-1-1
χ1922222222-2-2222222200222220022220-2-2-2-2-2-2-12-2-2-100000000-2-20000-100020200000-2-200000000-1-1-1-1-10000-11111
χ2022222222-2-222222220022-2-220022220-2-2-2-2-2-2-1-222-100000000-2-20000-1000-20-2000002200000000-111-1-100001-1-111
χ212222-2-2222i−2i222-2-2-2200-2222200-22-2-202i2i2i−2i−2i−2i-1-22i−2i-1000000002i−2i0000-1000-202000002i−2i00000000-1-1-11100001−ii−ii
χ222222-2-2222i−2i222-2-2-2200-22-2-2200-22-2-202i2i2i−2i−2i−2i-12−2i2i-1000000002i−2i0000-100020-200000−2i2i00000000-111110000-1i−i−ii
χ232222-2-222−2i2i222-2-2-2200-2222200-22-2-20−2i−2i−2i2i2i2i-1-2−2i2i-100000000−2i2i0000-1000-20200000−2i2i00000000-1-1-11100001i−ii−i
χ242222-2-222−2i2i222-2-2-2200-22-2-2200-22-2-20−2i−2i−2i2i2i2i-122i−2i-100000000−2i2i0000-100020-2000002i−2i00000000-111110000-1−iii−i
χ25222-22-22200-222-2-22222-2200-2222-22-2200000020002-2200-2-22-20022-2-220000000000000000000-22-2002-2000000000
χ26222-22-22200-222-2-222-2-2-2200-2-2-22-22-2-2000000200022-20022-2200-2-222200000000000000000002-2-2002-2000000000
χ27222-2-222200-22222-22222200-222-2-2-22200000020002-2-2002-2-2200222220000000000000000000-2-2-200-22000000000
χ28222-2-222200-22222-22-2-22200-2-2-2-2-2-22-2000000200022200-222-200-2-2-2-22000000000000000000022-200-22000000000
χ2933333333333-1-1-1-13-1113-133-111-1-1-1-113-1-13-1-10333011111111-1-1-1-1-1-10111-11-11-1-1-1-1-1-1111111-1-100000-1-1-1-100000
χ3033333333333-1-1-1-13-1113-1-3-3-111-1-1-1-113-1-13-1-10-3-3-3011-1-11111-1-1-1-1-1-10-1-1-11-11-1-1-1-1-111-1-11111-1-100000111100000
χ3133333333333-1-1-1-13-1-1-13-133-1-1-1-1-1-1-1-13-1-13-1-103330-1-1-1-1-1-1-1-1-1-111110-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11100000111100000
χ3233333333333-1-1-1-13-1-1-13-1-3-3-1-1-1-1-1-1-1-13-1-13-1-10-3-3-30-1-111-1-1-1-1-1-111110111111111111111-1-1-1-11100000-1-1-1-100000
χ3333333333-3-33-1-1-1-13-1113-133-111-1-1-1-11-311-31103-3-301111111111-1-1-1-101-1-1-11-11111111-1-1-1-1-1-1-1-100000-1-11100000
χ3433333333-3-33-1-1-1-13-1113-1-3-3-111-1-1-1-11-311-3110-333011-1-1111111-1-1-1-10-1111-11-11111-1-111-1-1-1-1-1-10000011-1-100000
χ3533333333-3-33-1-1-1-13-1-1-13-133-1-1-1-1-1-1-1-1-311-31103-3-30-1-1-1-1-1-1-1-11111110-111-1-1-1-1-1-1-1-111111111110000011-1-100000
χ3633333333-3-33-1-1-1-13-1-1-13-1-3-3-1-1-1-1-1-1-1-1-311-3110-3330-1-111-1-1-1-111111101-1-11111-1-1-1-1-1-1-1-111111100000-1-11100000
χ373333-3-3333i−3i3-1-111-3-111-3-133-1111-11113i−i−i−3iii0-33i−3i01-111-11-1-1−ii-1-1110-1i−i1-1-11−i−iii−iii−ii−ii−i-1100000-11−ii00000
χ383333-3-3333i−3i3-1-111-3-111-3-1-3-3-1111-11113i−i−i−3iii03−3i3i01-1-1-1-11-1-1−ii-1-11101−ii-111-1−i−iiii−i−iii−ii−i-11000001-1i−i00000
χ393333-3-3333i−3i3-1-111-3-1-1-1-3-133-1-1-11-111-13i−i−i−3iii0-33i−3i0-11-1-11-111−ii11-1-101−ii11-1-1ii−i−i−ii−ii−ii−ii1-1000001-1i−i00000
χ403333-3-3333i−3i3-1-111-3-1-1-1-3-1-3-3-1-1-11-111-13i−i−i−3iii03−3i3i0-11111-111−ii11-1-10-1i−i-1-111ii−i−ii−ii−i−ii−ii1-100000-11−ii00000
χ413333-3-333−3i3i3-1-111-3-111-3-133-1111-1111−3iii3i−i−i0-3−3i3i01-111-11-1-1i−i-1-1110-1−ii1-1-11ii−i−ii−i−ii−ii−ii-1100000-11i−i00000
χ423333-3-333−3i3i3-1-111-3-111-3-1-3-3-1111-1111−3iii3i−i−i033i−3i01-1-1-1-11-1-1i−i-1-11101i−i-111-1ii−i−i−iii−i−ii−ii-11000001-1−ii00000
χ433333-3-333−3i3i3-1-111-3-1-1-1-3-133-1-1-11-111-1−3iii3i−i−i0-3−3i3i0-11-1-11-111i−i11-1-101i−i11-1-1−i−iiii−ii−ii−ii−i1-1000001-1−ii00000
χ443333-3-333−3i3i3-1-111-3-1-1-1-3-1-3-3-1-1-11-111-1−3iii3i−i−i033i−3i0-11111-111i−i11-1-10-1−ii-1-111−i−iii−ii−iii−ii−i1-100000-11i−i00000
χ45444-44-44400-444-4-44400-4400-4004-44-40000000-2000-200000000000000-2000000000000000000000200-22000000000
χ46444-4-444400-44444-44004400-400-4-4-440000000-2000-200000000000000-20000000000000000000002002-2000000000
χ4744-4000-440004-4000-444040004-40000-40000004000400000000004-400-400000000000000000000000000000000000
χ4844-4000-440004-4000-4-4-404000-4400004000000400040000000000-4400-400000000000000000000000000000000000
χ49666666-2-266-222-2-2-2-200-2-2002002-2-220-2-2-2-2-2-2000000022000022000002220-20-2000000-2-200000000000000000000
χ50666666-2-266-222-2-2-2-200-2-2002002-2-220-2-2-2-2-2-20000000-2-200002200000-2-2-202020000002200000000000000000000
χ51666666-2-266-2-2-222-2222-2200-2-2-2-222-22-222-22200000-2-200-2222-2-200000000000000000000-2-2220000000000000000
χ52666666-2-266-2-2-222-22-2-2-2200-222-222-2-2-222-2220000022002-2-2-2-2-20000000000000000000022-2-20000000000000000
χ53666666-2-2-6-6-222-2-2-2-200-2-2002002-2-2202222220000000220000-2-2000002-2-20-20-20000002200000000000000000000
χ54666666-2-2-6-6-222-2-2-2-200-2-2002002-2-2202222220000000-2-20000-2-200000-2220202000000-2-200000000000000000000
χ55666666-2-2-6-6-2-2-222-2222-2200-2-2-2-222-222-2-22-2-200000-2-200-2222220000000000000000000022-2-20000000000000000
χ56666666-2-2-6-6-2-2-222-22-2-2-2200-222-222-2-22-2-22-2-20000022002-2-2-22200000000000000000000-2-2220000000000000000
χ576666-6-6-2-26i−6i-222222-2002-200200-2-22-20−2i−2i−2i2i2i2i00000002200002i−2i00000-22i−2i020-2000000−2i2i00000000000000000000
χ586666-6-6-2-26i−6i-222222-2002-200200-2-22-20−2i−2i−2i2i2i2i0000000-2-200002i−2i000002−2i2i0-2020000002i−2i00000000000000000000
χ596666-6-6-2-26i−6i-2-2-2-2-222222200-2-2-222-222−2i2i2i2i−2i−2i00000-220022-2-2−2i2i00000000000000000000−2i2i2i−2i0000000000000000
χ606666-6-6-2-26i−6i-2-2-2-2-222-2-22200-22222-22-2−2i2i2i2i−2i−2i000002-200-2-222−2i2i000000000000000000002i−2i−2i2i0000000000000000
χ616666-6-6-2-2−6i6i-222222-2002-200200-2-22-202i2i2i−2i−2i−2i0000000220000−2i2i00000-2−2i2i020-20000002i−2i00000000000000000000
χ626666-6-6-2-2−6i6i-222222-2002-200200-2-22-202i2i2i−2i−2i−2i0000000-2-20000−2i2i0000022i−2i0-202000000−2i2i00000000000000000000
χ636666-6-6-2-2−6i6i-2-2-2-2-222222200-2-2-222-2222i−2i−2i−2i2i2i00000-220022-2-22i−2i000000000000000000002i−2i−2i2i0000000000000000
χ646666-6-6-2-2−6i6i-2-2-2-2-222-2-22200-22222-22-22i−2i−2i−2i2i2i000002-200-2-2222i−2i00000000000000000000−2i2i2i−2i0000000000000000
χ65666-66-66600-6-2-2226-222-6-200222-22-22200000000000-2200-2-22-200-2-222000000000000000000002-200000000000000
χ66666-66-66600-6-2-2226-2-2-2-6-2002-2-2-22-22-2000000000002-20022-220022-2-200000000000000000000-2200000000000000
χ67666-66-6-2-2002-2-2-2-2-222222002-2-2-2-222204i−4i04i−4i000002-2002-22-2000000000000002i−2i2i−2i000000000000000000000000
χ68666-66-6-2-2002-2-2-2-2-222222002-2-2-2-22220−4i4i0−4i4i000002-2002-22-200000000000000−2i2i−2i2i000000000000000000000000
χ69666-66-6-2-2002-2-2-2-2-22-2-22200222-2-222-204i−4i04i−4i00000-2200-22-2200000000000000−2i2i−2i2i000000000000000000000000
χ70666-66-6-2-2002-2-2-2-2-22-2-22200222-2-222-20−4i4i0−4i4i00000-2200-22-22000000000000002i−2i2i−2i000000000000000000000000
χ71666-6-666600-6-2-2-2-2-6-2226-200222222-2200000000000-2-2002-2-2200-2-2-2-2000000000000000000002200000000000000
χ72666-6-666600-6-2-2-2-2-6-2-2-26-2002-2-2222-2-2000000000002200-222-200222200000000000000000000-2-200000000000000
χ73666-6-66-2-2002-2-2222222-22002-2-22-2-2-2204-40-44000002200-2-2-22000000000000002-2-22000000000000000000000000
χ74666-6-66-2-2002-2-2222222-22002-2-22-2-2-220-4404-4000002200-2-2-2200000000000000-222-2000000000000000000000000
χ75666-6-66-2-2002-2-22222-2-2-22002222-2-2-2-204-40-4400000-2-200222-200000000000000-222-2000000000000000000000000
χ76666-6-66-2-2002-2-22222-2-2-22002222-2-2-2-20-4404-400000-2-200222-2000000000000002-2-22000000000000000000000000
χ7788-8000-880008-8000-800080000000000000000-4000-400000000000000400000000000000000000000000000000000
χ78121212-1212-12-4-40044444-4-4004-400-40044-4-400000000000000000000000000000000000000000000000000000000000000
χ79121212-12-1212-4-400444-4-44-400-4-400-400-444400000000000000000000000000000000000000000000000000000000000000
χ801212-120004-4000-448-80-44404000-440000-4000000000000000000000004-4000000000000000000000000000000000000
χ811212-120004-4000-448-80-4-4-4040004-40000400000000000000000000000-44000000000000000000000000000000000000
χ821212-120004-4000-44-880-44404000-440000-400000000000000000000000-44000000000000000000000000000000000000
χ831212-120004-4000-44-880-4-4-4040004-400004000000000000000000000004-4000000000000000000000000000000000000
χ841212-12000-1212000-440004440-40004-40000-4000000000000000000000-4400000000000000000000000000000000000000
χ851212-12000-1212000-440004-4-40-4000-44000040000000000000000000004-400000000000000000000000000000000000000
χ8616-160000000000000008-8004-4000000000000004000-4004-40000000000000000000000000000000002-200000000000
χ8716-160000000000000008-800-44000000000000004000-400-44000000000000000000000000000000000-2200000000000
χ8816-16000000000000000-88004-4000000000000004000-400-440000000000000000000000000000000002-200000000000
χ8916-16000000000000000-8800-44000000000000004000-4004-4000000000000000000000000000000000-2200000000000
χ902424-240008-80008-80008000-800000000000000000000000000000000000000000000000000000000000000000000000
χ9132-3200000000000000000008-800000000000000-400040000000000000000000000000000000000000-2200000000000
χ9232-320000000000000000000-8800000000000000-4000400000000000000000000000000000000000002-200000000000

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