Finite Group Databasebeta

← Group #13180860

Character table — Group #13180860

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size11222222244444668812121212161616161616161616161616161616161618181818242436363636363636363636365454727272727272144144
order12233666636666443612121212333366666666666662488121222248882424242424666122424612
χ1111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111
χ3111111111111111111111111111111111111111-1-1111111-1-11-1-11111-1-1-111-1-1-1-1-1
χ4111111111111111111111111111111111111111-1-1-1-111-1-111-111-1-1-1-1-1-11-1-1111-1-1
χ511-111-1-1111-1-1-11-1111-1-1111111-11111-1-1-1-1-1-1-1-11-1111-11-11-1-11-111-1-1-1111-1-11-11-1
χ611-111-1-1111-1-1-11-1111-1-1111111-11111-1-1-1-1-1-1-1-11-1-1-11-1-11-111-11-1-111-11-1-111-111-1
χ711-111-1-1111-1-1-11-1111-1-1111111-11111-1-1-1-1-1-1-1-1-11111-11-1-11-1-1111-1-11-1-11-11-11-11
χ811-111-1-1111-1-1-11-1111-1-1111111-11111-1-1-1-1-1-1-1-1-11-1-11-1-111-111-1-1-1111-11-11-11-1-11
χ92222222222222222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12200220000000000022000000-1-1
χ102222222222222222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2002200000000000-2-200000011
χ112222-1-1-1-12-12-1-1-12222-12-122-1-1-122-1-1-122-1-1-1-1-1-10022-1-12200200-1-1-1-1000-1-100000
χ122222-1-1-1-12-12-1-1-12222-12-122-1-1-122-1-1-122-1-1-1-1-1-100-2-2-1-1-2-200-20011110001100000
χ13222-12222-1-1-1-1-1-122222-12-1-12-1-12-12-1-1-1-122-1-1-1-10000-1-10022022000000-100-1-1-100
χ14222-12222-1-1-1-1-1-122222-12-1-12-1-12-12-1-1-1-122-1-1-1-10000-1-100-2-20-2-200000010011100
χ1522-222-2-2222-2-2-22-22-1-1-2-222-1-1-1-11-1-1-1-1111111112-2002-200000000000-22000000-11
χ1622-222-2-2222-2-2-22-22-1-1-2-222-1-1-1-11-1-1-1-111111111-22002-2000000000002-20000001-1
χ1722-22-111-12-1-211-1-22221-2-122-1-1-1-22-1-1-1-2-21111110022-112-200-200-1-111000-1100000
χ1822-22-111-12-1-211-1-22221-2-122-1-1-1-22-1-1-1-2-211111100-2-2-11-220020011-1-10001-100000
χ1922-2-12-2-22-1-1111-1-2222-212-1-12-1-1-2-12-1-111-2-211110000-11002-202-2000000-1001-1100
χ2022-2-12-2-22-1-1111-1-2222-212-1-12-1-1-2-12-1-111-2-211110000-1100-220-22000000100-11-100
χ2133333333333333-1-100-1-1-1-1000000000000000003311-1-1-1-1-1-11111111-1-1-1-1-1-11100
χ2233333333333333-1-100-1-1-1-10000000000000000033-1-1-1-11111-1-1-1-1-1-1-1-1-11111-1-100
χ2333333333333333-1-100-1-1-1-100000000000000000-3-311-1-1-1-1111-1-11111111-1-11-1-100
χ2433333333333333-1-100-1-1-1-100000000000000000-3-3-1-1-1-111-1-1-111-1-1-1-111-111-11100
χ2533-333-3-3333-3-3-331-10011-1-1000000000000000003-311-11-11-11-11-111-1-11-1-1-1111-100
χ2633-333-3-3333-3-3-331-10011-1-1000000000000000003-3-1-1-111-11-11-11-1-1111-111-1-1-1100
χ2733-333-3-3333-3-3-331-10011-1-100000000000000000-3311-11-111-1-1-1111-1-1-111-11-1-1100
χ2833-333-3-3333-3-3-331-10011-1-100000000000000000-33-1-1-111-1-1111-1-1-111-11-11-111-100
χ294444-2-2-2-24-24-2-2-244-2-2-24-24-2111-2-2111-2-21111110000-2-2000000000000000000000
χ30444-24444-2-2-2-2-2-244-2-24-24-21-211-21-21111-2-211110000-2-2000000000000000000000
χ31444-2-2-2-2-2-21-21114444-2-2-2-2-2-2114-2-211-2-2-2-21111000011000000000000000000000
χ32444-2-2-2-2-2-21-211144-2-2-2-2-2-211−1−3i32−1+3i32-211−1−3i32−1+3i321111−1−3i32−1−3i32−1+3i32−1+3i32000011000000000000000000000
χ33444-2-2-2-2-2-21-211144-2-2-2-2-2-211−1+3i32−1−3i32-211−1+3i32−1−3i321111−1+3i32−1+3i32−1−3i32−1−3i32000011000000000000000000000
χ3444-44-222-24-2-422-2-44-2-22-4-24-21112-211122-1-1-1-1-1-10000-22000000000000000000000
χ3544-4-24-4-44-2-2222-2-44-2-2-424-21-21121-211-1-122-1-1-1-10000-22000000000000000000000
χ3644-4-2-222-2-212-1-11-444422-2-2-2-211-4-2-2112222-1-1-1-100001-1000000000000000000000
χ3744-4-2-222-2-212-1-11-44-2-222-2-211−1−3i32−1+3i32211−1−3i32−1+3i32-1-1-1-11+3i321+3i321−3i321−3i3200001-1000000000000000000000
χ3844-4-2-222-2-212-1-11-44-2-222-2-211−1+3i32−1−3i32211−1+3i32−1−3i32-1-1-1-11−3i321−3i321+3i321+3i3200001-1000000000000000000000
χ394-404400-4-44000-400-220000-2-2-2-2022220000000000−2i22i2000000000−2i22i2000000000000
χ404-404400-4-44000-400-220000-2-2-2-20222200000000002i2−2i20000000002i2−2i2000000000000
χ414-404-2−2i32i32-4-20−2i32i3200-220000-211102-1-1-100−i3i3−i3i3−i3i300−2i22i2000000000i2−i26−60000000000
χ424-404-2−2i32i32-4-20−2i32i3200-220000-211102-1-1-100−i3i3−i3i3−i3i3002i2−2i2000000000−i2i2−660000000000
χ434-404-22i3−2i32-4-202i3−2i3200-220000-211102-1-1-100i3−i3i3−i3i3−i300−2i22i2000000000i2−i2−660000000000
χ444-404-22i3−2i32-4-202i3−2i3200-220000-211102-1-1-100i3−i3i3−i3i3−i3002i2−2i2000000000−i2i26−60000000000
χ456666-3-3-3-36-36-3-3-3-2-2001-21-200000000000000000002211-2-200200-1-1-1-10001100000
χ466666-3-3-3-36-36-3-3-3-2-2001-21-20000000000000000000-2-2112200-2001111000-1-100000
χ47666-36666-3-3-3-3-3-3-2-200-21-210000000000000000000001100220-2-2000000-100-11100
χ48666-36666-3-3-3-3-3-3-2-200-21-210000000000000000000001100-2-20220000001001-1-100
χ4966-66-333-36-3-633-32-200-121-20000000000000000000221-1-2200-200-1-1110001-100000
χ5066-66-333-36-3-633-32-200-121-20000000000000000000-2-21-12-20020011-1-1000-1100000
χ5166-6-36-6-66-3-3333-32-2002-1-210000000000000000000001-1002-20-22000000-10011-100
χ5266-6-36-6-66-3-3333-32-2002-1-210000000000000000000001-100-2202-2000000100-1-1100
χ538-808800-8-88000-8002-2000022220-2-2-2-200000000000000000000000000000000000
χ548-808-4−4i34i34-8-40−4i34i34002-200002-1-1-10-211100i3−i3i3−i3i3−i3000000000000000000000000000
χ558-808-44i3−4i34-8-404i3−4i34002-200002-1-1-10-211100−i3i3−i3i3−i3i3000000000000000000000000000
χ568-80-4800-84-40004002-20000-12-1-101-2113-3003-3-33000000000000000000000000000
χ578-80-4800-84-40004002-20000-12-1-101-211-3300-333-3000000000000000000000000000
χ588-80-4800-84-4000400-4400002-4220-24-2-200000000000000000000000000000000000
χ598-80-4-4−4i34i344202i3−2i3-2002-20000-1-11−3i321+3i32011−1+3i32−1−3i32-33i3−i33−i32−3+i32−3−i323+i32000000000000000000000000000
χ608-80-4-4−4i34i344202i3−2i3-2002-20000-1-11+3i321−3i32011−1−3i32−1+3i323-3i3−i3−3−i323+i323−i32−3+i32000000000000000000000000000
χ618-80-4-4−4i34i344202i3−2i3-200-44000022-1-10-2-21100−2i32i3i3−i3i3−i3000000000000000000000000000
χ628-80-4-44i3−4i34420−2i32i3-2002-20000-1-11−3i321+3i32011−1+3i32−1−3i323-3−i3i3−3+i323−i323+i32−3−i32000000000000000000000000000
χ638-80-4-44i3−4i34420−2i32i3-2002-20000-1-11+3i321−3i32011−1−3i32−1+3i32-33−i3i33+i32−3−i32−3+i323−i32000000000000000000000000000
χ648-80-4-44i3−4i34420−2i32i3-200-44000022-1-10-2-211002i3−2i3−i3i3−i3i3000000000000000000000000000
χ65121212-6-6-6-6-6-63-6333-4-4002222000000000000000000000-1-1000000000000000000000
χ661212-12-6-666-6-636-3-334-400-2-222000000000000000000000-11000000000000000000000

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