Finite Group Databasebeta

← Group #72253783

Character table — Group #72253783

Order 2916.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size1222224444666612121212121212121212121212121212181818363636363636363636363636818181162162162162162162162162162162162162
order133333333333333333333333333333999999999999999222666666666181818
χ1111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111-11-1-1-1-1-11-1-1-1-1111
χ4111111111111111111111111111111111111111111111-1-11-1-1-1-1-11111-1-1-1
χ5222222222222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1020000020000-1-1-1
χ6222222222222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10-200000-20000111
χ722222222222-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1002000002-1-1-1000
χ822222222222-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-100-200000-2111000
χ92222222222-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-1222-1-1-1222-1-1-1-1-1-100200000-12-1-1000
χ102222222222-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-1222-1-1-1222-1-1-1-1-1-100-2000001-211000
χ112222222222-1-12-1-1-1-1-1-1-1-1-12222-1-1-1-1222-1-1-1-1-1-1222-1-1-100200000-1-12-1000
χ122222222222-1-12-1-1-1-1-1-1-1-1-12222-1-1-1-1222-1-1-1-1-1-1222-1-1-100-20000011-21000
χ132222222222-1-1-12-1-1-1-1-1-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1-122200200000-1-1-12000
χ142222222222-1-1-12-1-1-1-1-1-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1-122200-200000111-2000
χ1522222-1-1-1-1-122222-1-1-12-1-1-12-1-1-12-1-1-1ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ50200000-10000ζ+ζ8ζ2+ζ7ζ4+ζ5
χ1622222-1-1-1-1-122222-1-1-12-1-1-12-1-1-12-1-1-1ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ50-20000010000−ζ−ζ8−ζ2−ζ7−ζ4−ζ5
χ1722222-1-1-1-1-122222-1-1-12-1-1-12-1-1-12-1-1-1ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ80200000-10000ζ2+ζ7ζ4+ζ5ζ+ζ8
χ1822222-1-1-1-1-122222-1-1-12-1-1-12-1-1-12-1-1-1ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ80-20000010000−ζ2−ζ7−ζ4−ζ5−ζ−ζ8
χ1922222-1-1-1-1-122222-1-1-12-1-1-12-1-1-12-1-1-1ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ70200000-10000ζ4+ζ5ζ+ζ8ζ2+ζ7
χ2022222-1-1-1-1-122222-1-1-12-1-1-12-1-1-12-1-1-1ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ70-20000010000−ζ4−ζ5−ζ−ζ8−ζ2−ζ7
χ2144444444444-2-2-24444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2111111111000000000000000
χ224444444444-24-2-2-2-2-2-24444-2-2-2-2-2-2-2-2-2-2-2111-2-2-2111111000000000000000
χ234444444444-2-24-2-2-2-2-2-2-2-2-24444-2-2-2-2-2-2-2111111-2-2-2111000000000000000
χ244444444444-2-2-24-2-2-2-2-2-2-2-2-2-2-2-24444-2-2-2111111111-2-2-2000000000000000
χ2544444-2-2-2-2-24-2-2-24-2-2-2-2111-2111-21112ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ4+2ζ5−ζ−ζ8−ζ2−ζ7−ζ4−ζ5−ζ−ζ8−ζ2−ζ7−ζ4−ζ5−ζ−ζ8−ζ2−ζ7−ζ4−ζ5000000000000000
χ2644444-2-2-2-2-24-2-2-24-2-2-2-2111-2111-21112ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ+2ζ8−ζ2−ζ7−ζ4−ζ5−ζ−ζ8−ζ2−ζ7−ζ4−ζ5−ζ−ζ8−ζ2−ζ7−ζ4−ζ5−ζ−ζ8000000000000000
χ2744444-2-2-2-2-24-2-2-24-2-2-2-2111-2111-21112ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ2+2ζ7−ζ4−ζ5−ζ−ζ8−ζ2−ζ7−ζ4−ζ5−ζ−ζ8−ζ2−ζ7−ζ4−ζ5−ζ−ζ8−ζ2−ζ7000000000000000
χ2844444-2-2-2-2-2-24-2-2-21114-2-2-2-2111-21112ζ+2ζ82ζ2+2ζ72ζ4+2ζ5−ζ−ζ8−ζ2−ζ7−ζ4−ζ52ζ+2ζ82ζ2+2ζ72ζ4+2ζ5−ζ−ζ8−ζ2−ζ7−ζ4−ζ5−ζ−ζ8−ζ2−ζ7−ζ4−ζ5000000000000000
χ2944444-2-2-2-2-2-24-2-2-21114-2-2-2-2111-21112ζ2+2ζ72ζ4+2ζ52ζ+2ζ8−ζ2−ζ7−ζ4−ζ5−ζ−ζ82ζ2+2ζ72ζ4+2ζ52ζ+2ζ8−ζ2−ζ7−ζ4−ζ5−ζ−ζ8−ζ2−ζ7−ζ4−ζ5−ζ−ζ8000000000000000
χ3044444-2-2-2-2-2-24-2-2-21114-2-2-2-2111-21112ζ4+2ζ52ζ+2ζ82ζ2+2ζ7−ζ4−ζ5−ζ−ζ8−ζ2−ζ72ζ4+2ζ52ζ+2ζ82ζ2+2ζ7−ζ4−ζ5−ζ−ζ8−ζ2−ζ7−ζ4−ζ5−ζ−ζ8−ζ2−ζ7000000000000000
χ3144444-2-2-2-2-2-2-24-2-2111-21114-2-2-2-21112ζ+2ζ82ζ2+2ζ72ζ4+2ζ5−ζ−ζ8−ζ2−ζ7−ζ4−ζ5−ζ−ζ8−ζ2−ζ7−ζ4−ζ52ζ+2ζ82ζ2+2ζ72ζ4+2ζ5−ζ−ζ8−ζ2−ζ7−ζ4−ζ5000000000000000
χ3244444-2-2-2-2-2-2-24-2-2111-21114-2-2-2-21112ζ2+2ζ72ζ4+2ζ52ζ+2ζ8−ζ2−ζ7−ζ4−ζ5−ζ−ζ8−ζ2−ζ7−ζ4−ζ5−ζ−ζ82ζ2+2ζ72ζ4+2ζ52ζ+2ζ8−ζ2−ζ7−ζ4−ζ5−ζ−ζ8000000000000000
χ3344444-2-2-2-2-2-2-24-2-2111-21114-2-2-2-21112ζ4+2ζ52ζ+2ζ82ζ2+2ζ7−ζ4−ζ5−ζ−ζ8−ζ2−ζ7−ζ4−ζ5−ζ−ζ8−ζ2−ζ72ζ4+2ζ52ζ+2ζ82ζ2+2ζ7−ζ4−ζ5−ζ−ζ8−ζ2−ζ7000000000000000
χ3444444-2-2-2-2-2-2-2-24-2111-2111-21114-2-2-22ζ+2ζ82ζ2+2ζ72ζ4+2ζ5−ζ−ζ8−ζ2−ζ7−ζ4−ζ5−ζ−ζ8−ζ2−ζ7−ζ4−ζ5−ζ−ζ8−ζ2−ζ7−ζ4−ζ52ζ+2ζ82ζ2+2ζ72ζ4+2ζ5000000000000000
χ3544444-2-2-2-2-2-2-2-24-2111-2111-21114-2-2-22ζ2+2ζ72ζ4+2ζ52ζ+2ζ8−ζ2−ζ7−ζ4−ζ5−ζ−ζ8−ζ2−ζ7−ζ4−ζ5−ζ−ζ8−ζ2−ζ7−ζ4−ζ5−ζ−ζ82ζ2+2ζ72ζ4+2ζ52ζ+2ζ8000000000000000
χ3644444-2-2-2-2-2-2-2-24-2111-2111-21114-2-2-22ζ4+2ζ52ζ+2ζ82ζ2+2ζ7−ζ4−ζ5−ζ−ζ8−ζ2−ζ7−ζ4−ζ5−ζ−ζ8−ζ2−ζ7−ζ4−ζ5−ζ−ζ8−ζ2−ζ72ζ4+2ζ52ζ+2ζ82ζ2+2ζ7000000000000000
χ3766-3-3-366-3-3-30006000000000000-36-3-30000000000000002002-1-1-100000000
χ3866-3-3-366-3-3-30006000000000000-36-3-3000000000000000-200-211100000000
χ396-36-3-36-36-3-3006000000000-36-3-30000000000000000000200-12-1-100000000
χ406-36-3-36-36-3-3006000000000-36-3-30000000000000000000-2001-21100000000
χ416-3-36-36-3-36-306000000-36-3-300000000000000000000000200-1-12-100000000
χ426-3-36-36-3-36-306000000-36-3-300000000000000000000000-20011-2100000000
χ436-3-3-366-3-3-366000-36-3-3000000000000000000000000000200-1-1-1200000000
χ446-3-3-366-3-3-366000-36-3-3000000000000000000000000000-200111-200000000
χ451212-6-6-61212-6-6-6000-60000000000003-633000000000000000000000000000000
χ461212-6-6-6-6-633300012000000000000-6-633000000000000000000000000000000
χ471212-6-6-6-6-6333000-600000000000033−3+9i32−3−9i32000000000000000000000000000000
χ481212-6-6-6-6-6333000-600000000000033−3−9i32−3+9i32000000000000000000000000000000
χ4912-612-6-612-612-6-600-60000000003-6330000000000000000000000000000000000
χ5012-612-6-6-63-6330012000000000-6-6330000000000000000000000000000000000
χ5112-612-6-6-63-63300-600000000033−3+9i32−3−9i320000000000000000000000000000000000
χ5212-612-6-6-63-63300-600000000033−3−9i32−3+9i320000000000000000000000000000000000
χ5312-6-612-612-6-612-60-60000003-63300000000000000000000000000000000000000
χ5412-6-612-6-633-63012000000-6-63300000000000000000000000000000000000000
χ5512-6-612-6-633-630-600000033−3+9i32−3−9i3200000000000000000000000000000000000000
χ5612-6-612-6-633-630-600000033−3−9i32−3+9i3200000000000000000000000000000000000000
χ5712-6-6-61212-6-6-612-60003-633000000000000000000000000000000000000000000
χ5812-6-6-612-6333-612000-6-633000000000000000000000000000000000000000000
χ5912-6-6-612-6333-6-600033−3+9i32−3−9i32000000000000000000000000000000000000000000
χ6012-6-6-612-6333-6-600033−3−9i32−3+9i32000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 9 (ζ9 = 1); i = ζ2.