Finite Group DatabasebetaFinite Group Databasebeta| order | 36156 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×Dic393 |
| unambiguous semidirect product | C3⋊(C23×Dic131) |
| unambiguous semidirect product | C131⋊(Dic3×C23) |
| derived, Hall | C3×C131 ⋊ C4×C23 |
| Hall | C3×C23×C131 ⋊ C4 |
| Hall | C23×C131 ⋊ Dic3 |
| Sylow | C131 ⋊ Dic3×C23 |
| Hall | C3×C23 ⋊ Dic131 |
| Sylow | C3 ⋊ C23×Dic131 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C23 | D393 |
| commutator, hypocenter | C3×C131 | C4×C23 |
| Frattini | C2 | C23×D393 |
| Fitting, socle, prime radical | C2×C3×C23×C131 | C2 |
| cosocle | C2×C3×C131 | C2×C23 |
| LCS | G ▷ C3×C131 | |
| UCS | C1 ◁ C2×C23 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 36156 |
9108 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36156, 6);