Finite Group DatabasebetaFinite Group Databasebeta| order | 13572 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D3×D1131 |
| unambiguous semidirect product | (C3×D3)⋊D377 |
| unambiguous semidirect product | (D3×C13)⋊D87 |
| unambiguous semidirect product | (D3×C29)⋊D39 |
| Fitting, socle, derived, Hall | C32×C13×C29 ⋊ C22 |
| Hall | C13×C29 ⋊ D32 |
| Hall | C32×C29 ⋊ C2×D13 |
| Hall | C32×C13 ⋊ C2×D29 |
| Sylow | C29 ⋊ D3×D39 |
| Sylow | C13 ⋊ D3×D87 |
| Sylow | C32 ⋊ C2×D377 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C13×C29 | C22 |
| LCS | G ▷ C32×C13×C29 | |
| UCS | C1 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2262 |
1701 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13572, 136);