Finite Group DatabasebetaFinite Group Databasebeta| order | 13572 |
| isoclinism | isoclinic class of C3⋊#1181 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C13 · Schur multiplier (H2) = C1 |
| direct product | C3×C13×C3⋊#1181 |
| unambiguous semidirect product | C3⋊(C3×C13×#1181) |
| Fitting, socle, Hall | C32×C13×C29 ⋊ C4 |
| derived | C3×C29 ⋊ C3×C4×C13 |
| Hall | C13×C29 ⋊ C3×Dic3 |
| Hall | C32×C29 ⋊ C4×C13 |
| Hall | C32×C13 ⋊ #1181 |
| Sylow | C29 ⋊ C3×Dic3×C13 |
| Sylow | C32 ⋊ C13×#1181 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C13 | C3⋊#1181 |
| commutator, hypocenter | C3×C29 | C3×C4×C13 |
| Frattini | C1 | G |
| Fitting, socle | C32×C13×C29 | C4 |
| prime radical | C32×C13×D29 | C2 |
| cosocle | C3×D29 | C2×C3×C13 |
| LCS | G ▷ C3×C29 | |
| UCS | C1 ◁ C3×C13 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2262 |
1053 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13572, 108);