Finite Group Databasebeta

← Group #13048746

Character table — Group #13048746

Order 1296.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size11222222222444466666612121212121212121212121212121212121212121218182727363636363636363654545454545454108108
order12333346666121212123366121233333666661212121212121212121212442212121212121212124446612121212
χ1111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-11-1-11111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111
χ5111111-11111-1-1-1-11111-1-11111111111-1-1-1-1-1-1-1-1-1-1-11-1111111-1-1-1-1-11-111-1-11-1
χ6111111-11111-1-1-1-11111-1-11111111111-1-1-1-1-1-1-1-1-1-1-11-1-1-11111-1-1-1-11-11-1-111-11
χ7111111-11111-1-1-1-11111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-11111-1-1111-1-1-11
χ8111111-11111-1-1-1-11111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1111111-1-1-1111-1
χ92222222222222222-1-12-1-12-1-1-1-12-1-1-1-1222-1-1-1-1-1-1-1-1002200000000200-1-1-1-100
χ102222222222222222-1-12-1-12-1-1-1-12-1-1-1-1222-1-1-1-1-1-1-1-100-2-200000000-200111100
χ11222222222222222-122-122-12-1-1-1-12-1-1-1-1-1-122-1-1-1-1-1-10000000000000220000-1-1
χ12222222222222222-122-122-12-1-1-1-12-1-1-1-1-1-122-1-1-1-1-1-10000000000000-2-2000011
χ13222222-22222-2-2-2-22-1-12112-1-1-1-12-1-1-1-1-2-2-211111111002200000000-200-1-11100
χ14222222-22222-2-2-2-22-1-12112-1-1-1-12-1-1-1-1-2-2-21111111100-2-20000000020011-1-100
χ15222222-22222-2-2-2-2-122-1-2-2-12-1-1-1-12-1-1-1111-2-211111100000000000002-20000-11
χ16222222-22222-2-2-2-2-122-1-2-2-12-1-1-1-12-1-1-1111-2-21111110000000000000-2200001-1
χ17222-1-1-122-1-1-12-1-1-1222222-1-12-1-1-1-12-1-12-1-1-1-122-1-1-1-122002-1-1-12-1-1-1000000000
χ18222-1-1-122-1-1-12-1-1-1222222-1-12-1-1-1-12-1-12-1-1-1-122-1-1-1-1-2-200-2111-2111000000000
χ19222-1-1-1-22-1-1-1-21112222-2-2-1-12-1-1-1-12-1-1-21111-2-211112-2002-1-1-1-2111000000000
χ20222-1-1-1-22-1-1-1-21112222-2-2-1-12-1-1-1-12-1-1-21111-2-21111-2200-21112-1-1-1000000000
χ212-222220-2-2-2-2000022-2-20022222-2-2-2-2-200000000000002-2000000000002-20000
χ222-222220-2-2-2-2000022-2-20022222-2-2-2-2-20000000000000-2200000000000-220000
χ232-222220-2-2-2-200002-11-23−32-1-1-1-1-211110003−33−333−3−3002-200000000000-113−300
χ242-222220-2-2-2-200002-11-23−32-1-1-1-1-211110003−33−333−3−300-22000000000001-1−3300
χ252-222220-2-2-2-200002-11-2−332-1-1-1-1-21111000−33−33−3−333002-200000000000-11−3300
χ262-222220-2-2-2-200002-11-2−332-1-1-1-1-21111000−33−33−3−33300-22000000000001-13−300
χ27444444444444444-2-2-2-2-2-2-2-2111-2-2111-2-2-2-2-2111111000000000000000000000
χ28444444-44444-4-4-4-4-2-2-2-222-2-2111-2-211122222-1-1-1-1-1-1000000000000000000000
χ29444-2-2-244-2-2-24-2-2-24-2-24-2-2-21-211-21-2114-2-211-2-21111000000000000000000000
χ30444-2-2-244-2-2-24-2-2-2-244-2441-2-2111-2-211-211-2-2-2-21111000000000000000000000
χ31444-2-2-244-2-2-24-2-2-2-2-2-2-2-2-2111−1−3i32−1+3i32111−1−3i32−1+3i32-2111111−1−3i32−1+3i32−1−3i32−1+3i32000000000000000000000
χ32444-2-2-244-2-2-24-2-2-2-2-2-2-2-2-2111−1+3i32−1−3i32111−1+3i32−1−3i32-2111111−1+3i32−1−3i32−1+3i32−1−3i32000000000000000000000
χ33444-2-2-2-44-2-2-2-42224-2-2422-21-211-21-211-422-1-122-1-1-1-1000000000000000000000
χ34444-2-2-2-44-2-2-2-4222-244-2-4-41-2-2111-2-2112-1-12222-1-1-1-1000000000000000000000
χ35444-2-2-2-44-2-2-2-4222-2-2-2-222111−1−3i32−1+3i32111−1−3i32−1+3i322-1-1-1-1-1-11+3i321−3i321+3i321−3i32000000000000000000000
χ36444-2-2-2-44-2-2-2-4222-2-2-2-222111−1+3i32−1−3i32111−1+3i32−1−3i322-1-1-1-1-1-11−3i321+3i321−3i321+3i32000000000000000000000
χ374-444440-4-4-4-40000-24-4200-24-2-2-22-422200000000000000000000000000000000
χ384-444440-4-4-4-40000-2-22223−23-2-211122-1-1-100023−23−33−3−333000000000000000000000
χ394-444440-4-4-4-40000-2-222−2323-2-211122-1-1-1000−23233−333−3−3000000000000000000000
χ404-44-2-2-20-4222000044-4-400-2-24-2-222-42200000000000000000000000000000000
χ414-44-2-2-20-422200004-22-423−23-21-2112-12-1-1000−3323−23−3−333000000000000000000000
χ424-44-2-2-20-422200004-22-4−2323-21-2112-12-1-10003−3−232333−3−3000000000000000000000
χ434-44-2-2-20-42220000-24-42001-2-211-122-1-103i−3i00003i−3i−3i3i000000000000000000000
χ444-44-2-2-20-42220000-24-42001-2-211-122-1-10−3i3i0000−3i3i3i−3i000000000000000000000
χ454-44-2-2-20-42220000-2-22223−23111−1−3i32−1+3i32-1-1-11+3i321−3i3203i−3i−33−33ζ7+2ζ11−2ζ7−ζ11−ζ7−2ζ112ζ7+ζ11000000000000000000000
χ464-44-2-2-20-42220000-2-22223−23111−1+3i32−1−3i32-1-1-11−3i321+3i320−3i3i−33−33−2ζ7−ζ11ζ7+2ζ112ζ7+ζ11−ζ7−2ζ11000000000000000000000
χ474-44-2-2-20-42220000-2-222−2323111−1−3i32−1+3i32-1-1-11+3i321−3i320−3i3i3−33−3−ζ7−2ζ112ζ7+ζ11ζ7+2ζ11−2ζ7−ζ11000000000000000000000
χ484-44-2-2-20-42220000-2-222−2323111−1+3i32−1−3i32-1-1-11−3i321+3i3203i−3i3−33−32ζ7+ζ11−ζ7−2ζ11−2ζ7−ζ11ζ7+2ζ11000000000000000000000
χ4966-36-3-36-36-3-3-36-3-30000000000000000000000000002200-12-1-1-12-1-1000000000
χ5066-36-3-36-36-3-3-36-3-3000000000000000000000000000-2-2001-2111-211000000000
χ5166-36-3-3-6-36-3-33-6330000000000000000000000000002-200-12-1-11-211000000000
χ5266-36-3-3-6-36-3-33-633000000000000000000000000000-22001-211-12-1-1000000000
χ5366-3-36-36-3-36-3-3-36-30000000000000000000000000002200-1-12-1-1-12-1000000000
χ5466-3-36-36-3-36-3-3-36-3000000000000000000000000000-2-20011-2111-21000000000
χ5566-3-36-3-6-3-36-333-630000000000000000000000000002-200-1-12-111-21000000000
χ5666-3-36-3-6-3-36-333-63000000000000000000000000000-220011-21-1-12-1000000000
χ5766-3-3-366-3-3-36-3-3-360000000000000000000000000002200-1-1-12-1-1-12000000000
χ5866-3-3-366-3-3-36-3-3-36000000000000000000000000000-2-200111-2111-2000000000
χ5966-3-3-36-6-3-3-36333-60000000000000000000000000002-200-1-1-12111-2000000000
χ6066-3-3-36-6-3-3-36333-6000000000000000000000000000-2200111-2-1-1-12000000000
χ6112-12-612-6-606-12660000000000000000000000000000000000000000000000000000
χ6212-12-6-612-6066-1260000000000000000000000000000000000000000000000000000
χ6312-12-6-6-6120666-120000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.