Finite Group DatabasebetaFinite Group Databasebeta| order | 37100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C25 · Schur multiplier (H2) = C1 |
| direct product | C25×C7⋊#6157 |
| unambiguous semidirect product | C7⋊(C25×#6157) |
| Fitting, Hall | C7×C25×C53 ⋊ C4 |
| derived, Hall | C7×C53 ⋊ C4×C25 |
| Hall | C25×C53 ⋊ Dic7 |
| Hall | C7×C25 ⋊ #6157 |
| Sylow | C53 ⋊ C25×Dic7 |
| Sylow | C7 ⋊ C25×#6157 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | C7⋊#6157 |
| commutator, hypocenter | C7×C53 | C4×C25 |
| Frattini | C5 | C5×C7⋊#6157 |
| Fitting | C7×C25×C53 | C4 |
| socle | C5×C7×C53 | C4×C5 |
| prime radical, cosocle | C5×C7×D53 | C2×C5 |
| LCS | G ▷ C7×C53 | |
| UCS | C1 ◁ C25 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9275 |
2525 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37100, 11);