Finite Group DatabasebetaFinite Group Databasebeta| order | 37996 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C59 · Schur multiplier (H2) = C1 |
| direct product | C59×Dic161 |
| unambiguous semidirect product | C7⋊(C59×Dic23) |
| unambiguous semidirect product | C23⋊(Dic7×C59) |
| derived, Hall | C7×C23 ⋊ C4×C59 |
| Hall | C7×C23×C59 ⋊ C4 |
| Hall | C23×C59 ⋊ Dic7 |
| Hall | C7×C59 ⋊ Dic23 |
| Sylow | C23 ⋊ Dic7×C59 |
| Sylow | C7 ⋊ C59×Dic23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C59 | D161 |
| commutator, hypocenter | C7×C23 | C4×C59 |
| Frattini | C2 | C59×D161 |
| Fitting, socle, prime radical | C2×C7×C23×C59 | C2 |
| cosocle | C2×C7×C23 | C2×C59 |
| LCS | G ▷ C7×C23 | |
| UCS | C1 ◁ C2×C59 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 37996 |
9676 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37996, 7);