Finite Group DatabasebetaFinite Group Databasebeta| order | 31900 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C52 · Schur multiplier (H2) = C5 |
| direct product | C5×(C11⋊C5)⋊#1181 |
| unambiguous semidirect product | (C11⋊C5)⋊(C5×#1181) |
| unambiguous semidirect product | (C11⋊#1181)⋊C52 |
| unambiguous semidirect product | (C5×C11⋊#1181)⋊C5 |
| Fitting, socle | C5×C11×C29 ⋊ C4×C5 |
| derived, Hall | C11×C29 ⋊ C4×C52 |
| Hall | C5×C29×C11⋊C5 ⋊ C4 |
| Hall | C11⋊#1181 ⋊ C52 |
| Hall | C5×C11⋊C5 ⋊ #1181 |
| Sylow | C29 ⋊ C5×Dic11⋊C5 |
| Sylow | C11 ⋊ C52×#1181 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | (C11⋊C5)⋊#1181 |
| commutator, hypocenter | C11×C29 | C4×C52 |
| Frattini | C1 | G |
| Fitting, socle | C5×C11×C29 | C4×C5 |
| prime radical | C5×C11⋊C5×D29 | C2 |
| cosocle | C11×D29 | C2×C52 |
| LCS | G ▷ C11×C29 | |
| UCS | C1 ◁ C5 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1595 |
355 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31900, 68);