Finite Group DatabasebetaFinite Group Databasebeta| order | 37100 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D175⋊D53 |
| unambiguous semidirect product | D371⋊D25 |
| unambiguous semidirect product | D1325⋊D7 |
| Fitting, derived, Hall | C7×C25×C53 ⋊ C22 |
| Hall | C25×C53 ⋊ C2×D7 |
| Hall | C7×C53 ⋊ C2×D25 |
| Hall | C7×C25 ⋊ C2×D53 |
| Sylow | C53 ⋊ D7×D25 |
| Sylow | C25 ⋊ D7×D53 |
| Sylow | C7 ⋊ D25×D53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C7×C25×C53 | C22 |
| Frattini | C5 | D35⋊D53 |
| socle | C5×C7×C53 | C2×D5 |
| LCS | G ▷ C7×C25×C53 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9275 |
Polycyclic presentation:
2^2,5,7,53,5|c^5=f^4,d^a=d^6,e^a=e^52,c^b=c^4f,d^b=d^6,f^b=f^42384 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37100, 28);