Finite Group DatabasebetaFinite Group Databasebeta| order | 37996 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7×C23 · Schur multiplier (H2) = C1 |
| direct product | C7×C23×Dic59 |
| unambiguous semidirect product | C59⋊(C4×C7×C23) |
| derived, Sylow | C59 ⋊ C4×C7×C23 |
| Hall | C7×C23×C59 ⋊ C4 |
| Hall | C23×C59 ⋊ C4×C7 |
| Hall | C7×C59 ⋊ C4×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7×C23 | D59 |
| commutator, hypocenter | C59 | C4×C7×C23 |
| Frattini | C2 | C7×C23×D59 |
| Fitting, socle, prime radical | C2×C7×C23×C59 | C2 |
| cosocle | C2×C59 | C2×C7×C23 |
| LCS | G ▷ C59 | |
| UCS | C1 ◁ C2×C7×C23 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 37996 |
9982 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37996, 2);