Finite Group DatabasebetaFinite Group Databasebeta| order | 13572 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×#13094090⋊C3 |
| unambiguous semidirect product | #13094090⋊C32 |
| unambiguous semidirect product | (C3×#13094090)⋊C3 |
| Fitting, socle | C3×C13×C29 ⋊ C3×C4 |
| derived, Hall | C13×C29 ⋊ C32×C4 |
| Hall | C3×C29×C13⋊C3 ⋊ C4 |
| Hall | #13094090 ⋊ C32 |
| Hall | C3×C13⋊C3 ⋊ #1181 |
| Sylow | C29 ⋊ C3×Dic13⋊C3 |
| Sylow | C13 ⋊ C32×#1181 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #13094090⋊C3 |
| commutator, hypocenter | C13×C29 | C32×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C13×C29 | C3×C4 |
| prime radical | C3×C13⋊C3×D29 | C2 |
| cosocle | C13×D29 | C2×C32 |
| LCS | G ▷ C13×C29 | |
| UCS | C1 ◁ C3 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1131 |
195 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13572, 78);