Finite Group DatabasebetaFinite Group Databasebeta| order | 37100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C53 · Schur multiplier (H2) = C1 |
| direct product | C53×Dic175 |
| unambiguous semidirect product | C7⋊(C53×Dic25) |
| derived, Hall | C7×C25 ⋊ C4×C53 |
| Hall | C7×C25×C53 ⋊ C4 |
| Hall | C25×C53 ⋊ Dic7 |
| Hall | C7×C53 ⋊ Dic25 |
| Sylow | C25 ⋊ Dic7×C53 |
| Sylow | C7 ⋊ C53×Dic25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C53 | D175 |
| commutator, hypocenter | C7×C25 | C4×C53 |
| Frattini | C2×C5 | C53×D35 |
| Fitting | C2×C7×C25×C53 | C2 |
| socle, prime radical | C2×C5×C7×C53 | D5 |
| cosocle | C2×C7×C25 | C2×C53 |
| LCS | G ▷ C7×C25 | |
| UCS | C1 ◁ C2×C53 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 37100 |
9434 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37100, 7);