Finite Group DatabasebetaFinite Group Databasebeta| order | 37996 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D59×D161 |
| unambiguous semidirect product | (C7×D59)⋊D23 |
| unambiguous semidirect product | (C23×D59)⋊D7 |
| Fitting, socle, derived, Hall | C7×C23×C59 ⋊ C22 |
| Hall | C23×C59 ⋊ C2×D7 |
| Hall | C7×C59 ⋊ C2×D23 |
| Hall | C7×C23 ⋊ C2×D59 |
| Sylow | C59 ⋊ C2×D161 |
| Sylow | C23 ⋊ D7×D59 |
| Sylow | C7 ⋊ D23×D59 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C23×C59 | C22 |
| LCS | G ▷ C7×C23×C59 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9499 |
2542 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37996, 12);