Finite Group DatabasebetaFinite Group Databasebeta| order | 37100 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×D25×D53 |
| unambiguous semidirect product | (D25×C53)⋊(C2×C7) |
| unambiguous semidirect product | (C25×D53)⋊(C2×C7) |
| unambiguous semidirect product | D1325⋊(C2×C7) |
| Fitting, Hall | C7×C25×C53 ⋊ C22 |
| derived, Hall | C25×C53 ⋊ C22×C7 |
| Hall | C7×C53 ⋊ C2×D25 |
| Hall | C7×C25 ⋊ C2×D53 |
| Sylow | C53 ⋊ C2×C7×D25 |
| Sylow | C25 ⋊ C2×C7×D53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D25×D53 |
| commutator, cosocle, hypocenter | C25×C53 | C22×C7 |
| Frattini | C5 | C7×D5×D53 |
| Fitting | C7×C25×C53 | C22 |
| socle | C5×C7×C53 | C2×D5 |
| LCS | G ▷ C25×C53 | |
| UCS | C1 ◁ C7 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9275 |
2744 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37100, 22);