Finite Group DatabasebetaFinite Group Databasebeta| order | 27360 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 74317824 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26×C3 |
| abelian | C23×C32×C4×C5×C19 |
| multiplicative | (ℤ/52143)ˣ, (ℤ/52899)ˣ, (ℤ/56792)ˣ, (ℤ/59384)ˣ, (ℤ/59955)ˣ, (ℤ/60165)ˣ, (ℤ/63952)ˣ, (ℤ/69524)ˣ, (ℤ/70532)ˣ, (ℤ/79940)ˣ, (ℤ/82224)ˣ, (ℤ/85188)ˣ, (ℤ/89076)ˣ, (ℤ/89388)ˣ, (ℤ/90684)ˣ, (ℤ/102780)ˣ, (ℤ/104286)ˣ, (ℤ/105798)ˣ, (ℤ/119910)ˣ, (ℤ/120330)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C24×C32×C5×C19 |
| socle, prime radical | C24×C32×C5×C19 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
2832 conjugacy classes of subgroups.
27360 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.