Finite Group DatabasebetaFinite Group Databasebeta| order | 37100 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C5 |
| direct product | D53×C5⋊D35 |
| unambiguous semidirect product | (C5×D53)⋊D35 |
| unambiguous semidirect product | (C7×D53)⋊(C5⋊D5) |
| Fitting, socle, derived, Hall | C52×C7×C53 ⋊ C22 |
| Hall | C52×C53 ⋊ C2×D7 |
| Hall | C7×C53 ⋊ C2×C5⋊D5 |
| Hall | C52×C7 ⋊ C2×D53 |
| Sylow | C53 ⋊ C2×C5⋊D35 |
| Sylow | C52 ⋊ D7×D53 |
| Sylow | C7 ⋊ C5⋊D5×D53 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C7×C53 | C22 |
| LCS | G ▷ C52×C7×C53 | |
| UCS | C1 | |
160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9275 |
2492 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37100, 89);