Finite Group DatabasebetaFinite Group Databasebeta| order | 37100 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D265⋊D35 |
| Fitting, socle, derived, Hall | C52×C7×C53 ⋊ C22 |
| Hall | C52×C53 ⋊ C2×D7 |
| Hall | C7×C53 ⋊ D52 |
| Hall | C52×C7 ⋊ C2×D53 |
| Sylow | C53 ⋊ D5×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 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3710 |
Polycyclic presentation:
2^2,5^2,7,53|c^a=c^4,f^a=f^52,c^b=c^4,d^b=d^4,e^b=e^62390 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37100, 82);