Finite Group DatabasebetaFinite Group Databasebeta| order | 13572 |
| isoclinism | isoclinic class of A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C13×C29 · Schur multiplier (H2) = C2×C3 |
| Fitting, socle | C22×C3×C13×C29 ⋊ C3 |
| derived, Sylow | C22 ⋊ C32×C13×C29 |
| Hall | C22×C13×C29 ⋊ C32 |
| Hall | C22×C29 ⋊ C32×C13 |
| Hall | C22×C13 ⋊ C32×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C13×C29 | A4 |
| commutator, cosocle, hypocenter | C22 | C32×C13×C29 |
| Frattini | C1 | G |
| Fitting, socle | C22×C3×C13×C29 | C3 |
| LCS | G ▷ C22 | |
| UCS | C1 ◁ C3×C13×C29 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4524 |
4524 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13572, 153);