Finite Group DatabasebetaFinite Group Databasebeta| order | 37492 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×Dic721 |
| unambiguous semidirect product | C7⋊(C13×Dic103) |
| unambiguous semidirect product | C103⋊(C13×Dic7) |
| derived, Hall | C7×C103 ⋊ C4×C13 |
| Hall | C7×C13×C103 ⋊ C4 |
| Hall | C13×C103 ⋊ Dic7 |
| Sylow | C103 ⋊ C13×Dic7 |
| Hall | C7×C13 ⋊ Dic103 |
| Sylow | C7 ⋊ C13×Dic103 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C13 | D721 |
| commutator, hypocenter | C7×C103 | C4×C13 |
| Frattini | C2 | C13×D721 |
| Fitting, socle, prime radical | C2×C7×C13×C103 | C2 |
| cosocle | C2×C7×C103 | C2×C13 |
| LCS | G ▷ C7×C103 | |
| UCS | C1 ◁ C2×C13 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 37492 |
9412 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37492, 6);