Finite Group DatabasebetaFinite Group Databasebeta| order | 37492 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D13×D721 |
| unambiguous semidirect product | (C7×D13)⋊D103 |
| unambiguous semidirect product | (D13×C103)⋊D7 |
| Fitting, socle, derived, Hall | C7×C13×C103 ⋊ C22 |
| Hall | C13×C103 ⋊ C2×D7 |
| Hall | C7×C103 ⋊ C2×D13 |
| Sylow | C103 ⋊ D7×D13 |
| Hall | C7×C13 ⋊ C2×D103 |
| Sylow | C13 ⋊ C2×D721 |
| Sylow | C7 ⋊ D13×D103 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C13×C103 | C22 |
| LCS | G ▷ C7×C13×C103 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9373 |
2896 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37492, 18);