Finite Group DatabasebetaFinite Group Databasebeta| order | 37100 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C52 · Schur multiplier (H2) = C2×C5 |
| direct product | C52×D7×D53 |
| unambiguous semidirect product | (D7×C53)⋊(C2×C52) |
| unambiguous semidirect product | (C7×D53)⋊(C2×C52) |
| unambiguous semidirect product | D371⋊(C2×C52) |
| Fitting, socle, Hall | C52×C7×C53 ⋊ C22 |
| derived, Hall | C7×C53 ⋊ C22×C52 |
| Hall | C52×C53 ⋊ C2×D7 |
| Hall | C52×C7 ⋊ C2×D53 |
| Sylow | C53 ⋊ C2×C52×D7 |
| Sylow | C7 ⋊ C2×C52×D53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52 | D7×D53 |
| commutator, cosocle, hypocenter | C7×C53 | C22×C52 |
| Frattini | C1 | G |
| Fitting, socle | C52×C7×C53 | C22 |
| LCS | G ▷ C7×C53 | |
| UCS | C1 ◁ C52 | |
160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9275 |
3500 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37100, 51);