Finite Group DatabasebetaFinite Group Databasebeta| order | 1272 |
| isoclinism | isoclinic class of A4⋊D53 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | A4⋊D53 |
| unambiguous semidirect product | C53⋊S4 |
| Fitting, socle | C22×C53 ⋊ D3 |
| derived | A4×C53 ⋊ C2 |
| Sylow | C53 ⋊ S4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | A4×C53 | C2 |
| Fitting, socle | C22×C53 | D3 |
| LCS | G ▷ A4×C53 | |
| UCS | C1 | |
22 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 212 |
Polycyclic presentation:
2,3,53,2^2|b^a=b^2,c^a=c^52,d^a=de,d^b=e,e^b=de109 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1272, 35);