Finite Group DatabasebetaFinite Group Databasebeta| order | 37093 |
| automorphism | ? |
| homology | Abelianization (H1) = C72 · Schur multiplier (H2) = C7 |
| direct product | C7×C757⋊C7 |
| unambiguous semidirect product | C757⋊C72 |
| unambiguous semidirect product | (C7×C757)⋊C7 |
| Fitting, socle | C7×C757 ⋊ C7 |
| derived, Sylow | C757 ⋊ C72 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | C757⋊C7 |
| commutator, cosocle, hypocenter | C757 | C72 |
| Frattini | C1 | G |
| Fitting, socle | C7×C757 | C7 |
| LCS | G ▷ C757 | |
| UCS | C1 ◁ C7 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5299 |
805 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37093, 3);