Finite Group Databasebeta

← Group #11724061

Character table — Group #11724061

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48
size1333331616266666323226666632322666663232266666323292727272727144144
order122222333666663391818181818999181818181899918181818189922222266
χ1111111111111111111111111111111111111111111111111
χ2111111−1+i32−1−i32111111−1+i32−1−i32111111−1+i32−1−i32111111−1+i32−1−i32111111−1+i32−1−i32111111−1+i32−1−i32
χ3111111−1−i32−1+i32111111−1−i32−1+i32111111−1−i32−1+i32111111−1−i32−1+i32111111−1−i32−1+i32111111−1−i32−1+i32
χ433-1-1-1-10033-1-1-1-10033-1-1-1-10033-1-1-1-10033-1-1-1-10033-1-1-1-100
χ53-13-1-1-1003-13-1-1-1003-13-1-1-1003-13-1-1-1003-13-1-1-1003-13-1-1-100
χ63-1-13-1-1003-1-13-1-1003-1-13-1-1003-1-13-1-1003-1-13-1-1003-1-13-1-100
χ73-1-1-13-1003-1-1-13-1003-1-1-13-1003-1-1-13-1003-1-1-13-1003-1-1-13-100
χ83-1-1-1-13003-1-1-1-13003-1-1-1-13003-1-1-1-13003-1-1-1-13003-1-1-1-1300
χ91111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ10111111−1+i32−1−i32111111−1+i32−1−i32111111−1+i32−1−i32111111−1+i32−1−i32111111−1+i32−1−i32-1-1-1-1-1-11−i321+i32
χ11111111−1−i32−1+i32111111−1−i32−1+i32111111−1−i32−1+i32111111−1−i32−1+i32111111−1−i32−1+i32-1-1-1-1-1-11+i321−i32
χ1233-1-1-1-10033-1-1-1-10033-1-1-1-10033-1-1-1-10033-1-1-1-100-3-3111100
χ133-13-1-1-1003-13-1-1-1003-13-1-1-1003-13-1-1-1003-13-1-1-100-31-311100
χ143-1-13-1-1003-1-13-1-1003-1-13-1-1003-1-13-1-1003-1-13-1-100-311-31100
χ153-1-1-13-1003-1-1-13-1003-1-1-13-1003-1-1-13-1003-1-1-13-100-3111-3100
χ163-1-1-1-13003-1-1-1-13003-1-1-1-13003-1-1-1-13003-1-1-1-1300-31111-300
χ172222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000
χ18222222−1+i3−1−i3222222−1+i3−1−i3-1-1-1-1-1-11−i321+i32-1-1-1-1-1-11−i321+i32-1-1-1-1-1-11−i321+i3200000000
χ19222222−1−i3−1+i3222222−1−i3−1+i3-1-1-1-1-1-11+i321−i32-1-1-1-1-1-11+i321−i32-1-1-1-1-1-11+i321−i3200000000
χ2066-2-2-2-20066-2-2-2-200-3-3111100-3-3111100-3-311110000000000
χ216-26-2-2-2006-26-2-2-200-31-311100-31-311100-31-31110000000000
χ226-2-26-2-2006-2-26-2-200-311-31100-311-31100-311-3110000000000
χ236-2-2-26-2006-2-2-26-200-3111-3100-3111-3100-3111-310000000000
χ246-2-2-2-26006-2-2-2-2600-31111-300-31111-300-31111-30000000000
χ2522222222-1-1-1-1-1-1-1-1ζ+ζ8ζ+ζ8ζ+ζ8ζ+ζ8ζ+ζ8ζ+ζ8ζ+ζ8ζ+ζ8ζ2+ζ7ζ2+ζ7ζ2+ζ7ζ2+ζ7ζ2+ζ7ζ2+ζ7ζ2+ζ7ζ2+ζ7ζ4+ζ5ζ4+ζ5ζ4+ζ5ζ4+ζ5ζ4+ζ5ζ4+ζ5ζ4+ζ5ζ4+ζ500000000
χ26222222−1+i3−1−i3-1-1-1-1-1-11−i321+i32ζ+ζ8ζ+ζ8ζ+ζ8ζ+ζ8ζ+ζ8ζ+ζ8ζ2+ζ4ζ5+ζ7ζ2+ζ7ζ2+ζ7ζ2+ζ7ζ2+ζ7ζ2+ζ7ζ2+ζ7ζ+ζ5ζ4+ζ8ζ4+ζ5ζ4+ζ5ζ4+ζ5ζ4+ζ5ζ4+ζ5ζ4+ζ5ζ7+ζ8ζ+ζ200000000
χ27222222−1−i3−1+i3-1-1-1-1-1-11+i321−i32ζ+ζ8ζ+ζ8ζ+ζ8ζ+ζ8ζ+ζ8ζ+ζ8ζ5+ζ7ζ2+ζ4ζ2+ζ7ζ2+ζ7ζ2+ζ7ζ2+ζ7ζ2+ζ7ζ2+ζ7ζ4+ζ8ζ+ζ5ζ4+ζ5ζ4+ζ5ζ4+ζ5ζ4+ζ5ζ4+ζ5ζ4+ζ5ζ+ζ2ζ7+ζ800000000
χ2866-2-2-2-200-3-31111003ζ+3ζ83ζ+3ζ8−ζ−ζ8−ζ−ζ8−ζ−ζ8−ζ−ζ8003ζ2+3ζ73ζ2+3ζ7−ζ2−ζ7−ζ2−ζ7−ζ2−ζ7−ζ2−ζ7003ζ4+3ζ53ζ4+3ζ5−ζ4−ζ5−ζ4−ζ5−ζ4−ζ5−ζ4−ζ50000000000
χ296-26-2-2-200-31-3111003ζ+3ζ8−ζ−ζ83ζ+3ζ8−ζ−ζ8−ζ−ζ8−ζ−ζ8003ζ2+3ζ7−ζ2−ζ73ζ2+3ζ7−ζ2−ζ7−ζ2−ζ7−ζ2−ζ7003ζ4+3ζ5−ζ4−ζ53ζ4+3ζ5−ζ4−ζ5−ζ4−ζ5−ζ4−ζ50000000000
χ306-2-26-2-200-311-311003ζ+3ζ8−ζ−ζ8−ζ−ζ83ζ+3ζ8−ζ−ζ8−ζ−ζ8003ζ2+3ζ7−ζ2−ζ7−ζ2−ζ73ζ2+3ζ7−ζ2−ζ7−ζ2−ζ7003ζ4+3ζ5−ζ4−ζ5−ζ4−ζ53ζ4+3ζ5−ζ4−ζ5−ζ4−ζ50000000000
χ316-2-2-26-200-3111-31003ζ+3ζ8−ζ−ζ8−ζ−ζ8−ζ−ζ83ζ+3ζ8−ζ−ζ8003ζ2+3ζ7−ζ2−ζ7−ζ2−ζ7−ζ2−ζ73ζ2+3ζ7−ζ2−ζ7003ζ4+3ζ5−ζ4−ζ5−ζ4−ζ5−ζ4−ζ53ζ4+3ζ5−ζ4−ζ50000000000
χ326-2-2-2-2600-31111-3003ζ+3ζ8−ζ−ζ8−ζ−ζ8−ζ−ζ8−ζ−ζ83ζ+3ζ8003ζ2+3ζ7−ζ2−ζ7−ζ2−ζ7−ζ2−ζ7−ζ2−ζ73ζ2+3ζ7003ζ4+3ζ5−ζ4−ζ5−ζ4−ζ5−ζ4−ζ5−ζ4−ζ53ζ4+3ζ50000000000
χ3322222222-1-1-1-1-1-1-1-1ζ2+ζ7ζ2+ζ7ζ2+ζ7ζ2+ζ7ζ2+ζ7ζ2+ζ7ζ2+ζ7ζ2+ζ7ζ4+ζ5ζ4+ζ5ζ4+ζ5ζ4+ζ5ζ4+ζ5ζ4+ζ5ζ4+ζ5ζ4+ζ5ζ+ζ8ζ+ζ8ζ+ζ8ζ+ζ8ζ+ζ8ζ+ζ8ζ+ζ8ζ+ζ800000000
χ34222222−1+i3−1−i3-1-1-1-1-1-11−i321+i32ζ2+ζ7ζ2+ζ7ζ2+ζ7ζ2+ζ7ζ2+ζ7ζ2+ζ7ζ+ζ5ζ4+ζ8ζ4+ζ5ζ4+ζ5ζ4+ζ5ζ4+ζ5ζ4+ζ5ζ4+ζ5ζ7+ζ8ζ+ζ2ζ+ζ8ζ+ζ8ζ+ζ8ζ+ζ8ζ+ζ8ζ+ζ8ζ2+ζ4ζ5+ζ700000000
χ35222222−1−i3−1+i3-1-1-1-1-1-11+i321−i32ζ2+ζ7ζ2+ζ7ζ2+ζ7ζ2+ζ7ζ2+ζ7ζ2+ζ7ζ4+ζ8ζ+ζ5ζ4+ζ5ζ4+ζ5ζ4+ζ5ζ4+ζ5ζ4+ζ5ζ4+ζ5ζ+ζ2ζ7+ζ8ζ+ζ8ζ+ζ8ζ+ζ8ζ+ζ8ζ+ζ8ζ+ζ8ζ5+ζ7ζ2+ζ400000000
χ3666-2-2-2-200-3-31111003ζ2+3ζ73ζ2+3ζ7−ζ2−ζ7−ζ2−ζ7−ζ2−ζ7−ζ2−ζ7003ζ4+3ζ53ζ4+3ζ5−ζ4−ζ5−ζ4−ζ5−ζ4−ζ5−ζ4−ζ5003ζ+3ζ83ζ+3ζ8−ζ−ζ8−ζ−ζ8−ζ−ζ8−ζ−ζ80000000000
χ376-26-2-2-200-31-3111003ζ2+3ζ7−ζ2−ζ73ζ2+3ζ7−ζ2−ζ7−ζ2−ζ7−ζ2−ζ7003ζ4+3ζ5−ζ4−ζ53ζ4+3ζ5−ζ4−ζ5−ζ4−ζ5−ζ4−ζ5003ζ+3ζ8−ζ−ζ83ζ+3ζ8−ζ−ζ8−ζ−ζ8−ζ−ζ80000000000
χ386-2-26-2-200-311-311003ζ2+3ζ7−ζ2−ζ7−ζ2−ζ73ζ2+3ζ7−ζ2−ζ7−ζ2−ζ7003ζ4+3ζ5−ζ4−ζ5−ζ4−ζ53ζ4+3ζ5−ζ4−ζ5−ζ4−ζ5003ζ+3ζ8−ζ−ζ8−ζ−ζ83ζ+3ζ8−ζ−ζ8−ζ−ζ80000000000
χ396-2-2-26-200-3111-31003ζ2+3ζ7−ζ2−ζ7−ζ2−ζ7−ζ2−ζ73ζ2+3ζ7−ζ2−ζ7003ζ4+3ζ5−ζ4−ζ5−ζ4−ζ5−ζ4−ζ53ζ4+3ζ5−ζ4−ζ5003ζ+3ζ8−ζ−ζ8−ζ−ζ8−ζ−ζ83ζ+3ζ8−ζ−ζ80000000000
χ406-2-2-2-2600-31111-3003ζ2+3ζ7−ζ2−ζ7−ζ2−ζ7−ζ2−ζ7−ζ2−ζ73ζ2+3ζ7003ζ4+3ζ5−ζ4−ζ5−ζ4−ζ5−ζ4−ζ5−ζ4−ζ53ζ4+3ζ5003ζ+3ζ8−ζ−ζ8−ζ−ζ8−ζ−ζ8−ζ−ζ83ζ+3ζ80000000000
χ4122222222-1-1-1-1-1-1-1-1ζ4+ζ5ζ4+ζ5ζ4+ζ5ζ4+ζ5ζ4+ζ5ζ4+ζ5ζ4+ζ5ζ4+ζ5ζ+ζ8ζ+ζ8ζ+ζ8ζ+ζ8ζ+ζ8ζ+ζ8ζ+ζ8ζ+ζ8ζ2+ζ7ζ2+ζ7ζ2+ζ7ζ2+ζ7ζ2+ζ7ζ2+ζ7ζ2+ζ7ζ2+ζ700000000
χ42222222−1+i3−1−i3-1-1-1-1-1-11−i321+i32ζ4+ζ5ζ4+ζ5ζ4+ζ5ζ4+ζ5ζ4+ζ5ζ4+ζ5ζ7+ζ8ζ+ζ2ζ+ζ8ζ+ζ8ζ+ζ8ζ+ζ8ζ+ζ8ζ+ζ8ζ2+ζ4ζ5+ζ7ζ2+ζ7ζ2+ζ7ζ2+ζ7ζ2+ζ7ζ2+ζ7ζ2+ζ7ζ+ζ5ζ4+ζ800000000
χ43222222−1−i3−1+i3-1-1-1-1-1-11+i321−i32ζ4+ζ5ζ4+ζ5ζ4+ζ5ζ4+ζ5ζ4+ζ5ζ4+ζ5ζ+ζ2ζ7+ζ8ζ+ζ8ζ+ζ8ζ+ζ8ζ+ζ8ζ+ζ8ζ+ζ8ζ5+ζ7ζ2+ζ4ζ2+ζ7ζ2+ζ7ζ2+ζ7ζ2+ζ7ζ2+ζ7ζ2+ζ7ζ4+ζ8ζ+ζ500000000
χ4466-2-2-2-200-3-31111003ζ4+3ζ53ζ4+3ζ5−ζ4−ζ5−ζ4−ζ5−ζ4−ζ5−ζ4−ζ5003ζ+3ζ83ζ+3ζ8−ζ−ζ8−ζ−ζ8−ζ−ζ8−ζ−ζ8003ζ2+3ζ73ζ2+3ζ7−ζ2−ζ7−ζ2−ζ7−ζ2−ζ7−ζ2−ζ70000000000
χ456-26-2-2-200-31-3111003ζ4+3ζ5−ζ4−ζ53ζ4+3ζ5−ζ4−ζ5−ζ4−ζ5−ζ4−ζ5003ζ+3ζ8−ζ−ζ83ζ+3ζ8−ζ−ζ8−ζ−ζ8−ζ−ζ8003ζ2+3ζ7−ζ2−ζ73ζ2+3ζ7−ζ2−ζ7−ζ2−ζ7−ζ2−ζ70000000000
χ466-2-26-2-200-311-311003ζ4+3ζ5−ζ4−ζ5−ζ4−ζ53ζ4+3ζ5−ζ4−ζ5−ζ4−ζ5003ζ+3ζ8−ζ−ζ8−ζ−ζ83ζ+3ζ8−ζ−ζ8−ζ−ζ8003ζ2+3ζ7−ζ2−ζ7−ζ2−ζ73ζ2+3ζ7−ζ2−ζ7−ζ2−ζ70000000000
χ476-2-2-26-200-3111-31003ζ4+3ζ5−ζ4−ζ5−ζ4−ζ5−ζ4−ζ53ζ4+3ζ5−ζ4−ζ5003ζ+3ζ8−ζ−ζ8−ζ−ζ8−ζ−ζ83ζ+3ζ8−ζ−ζ8003ζ2+3ζ7−ζ2−ζ7−ζ2−ζ7−ζ2−ζ73ζ2+3ζ7−ζ2−ζ70000000000
χ486-2-2-2-2600-31111-3003ζ4+3ζ5−ζ4−ζ5−ζ4−ζ5−ζ4−ζ5−ζ4−ζ53ζ4+3ζ5003ζ+3ζ8−ζ−ζ8−ζ−ζ8−ζ−ζ8−ζ−ζ83ζ+3ζ8003ζ2+3ζ7−ζ2−ζ7−ζ2−ζ7−ζ2−ζ7−ζ2−ζ73ζ2+3ζ70000000000

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