Finite Group DatabasebetaFinite Group Databasebeta| order | 13572 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×#13094087 |
| Fitting, Hall | C9×C13×C29 ⋊ C4 |
| derived, Hall | C13×C29 ⋊ C4×C9 |
| Hall | C9×C29 ⋊ #261 |
| Hall | C9×C13 ⋊ #1181 |
| Sylow | C29 ⋊ C9×#261 |
| Sylow | C13 ⋊ C9×#1181 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | #13094087 |
| commutator, hypocenter | C13×C29 | C4×C9 |
| Frattini | C3 | C3×#13094087 |
| Fitting | C9×C13×C29 | C4 |
| socle | C3×C13×C29 | C3×C4 |
| prime radical, cosocle | C3×D377 | C2×C3 |
| LCS | G ▷ C13×C29 | |
| UCS | C1 ◁ C9 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3393 |
882 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13572, 26);