Finite Group DatabasebetaFinite Group Databasebeta| order | 13572 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C3⋊D1131 |
| unambiguous semidirect product | (C2×C3)⋊D1131 |
| unambiguous semidirect product | (C2×C13)⋊(C3⋊D87) |
| unambiguous semidirect product | (C2×C29)⋊(C3⋊D39) |
| Fitting, socle | C2×C32×C13×C29 ⋊ C2 |
| derived, Hall | C32×C13×C29 ⋊ C22 |
| Hall | C13×C29 ⋊ C2×C3⋊D3 |
| Hall | C32×C29 ⋊ C2×D13 |
| Hall | C32×C13 ⋊ C2×D29 |
| Sylow | C29 ⋊ C2×C3⋊D39 |
| Sylow | C13 ⋊ C2×C3⋊D87 |
| Sylow | C32 ⋊ C2×D377 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C3⋊D1131 |
| commutator, cosocle, hypocenter | C32×C13×C29 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C13×C29 | C2 |
| LCS | G ▷ C32×C13×C29 | |
| UCS | C1 ◁ C2 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6786 |
3396 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13572, 155);