Finite Group DatabasebetaFinite Group Databasebeta| order | 37100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊#19127086 |
| Fitting, socle, derived, Hall | C52×C7×C53 ⋊ C4 |
| Hall | C52×C53 ⋊ Dic7 |
| Hall | C7×C53 ⋊ #1042 |
| Hall | C52×C7 ⋊ #6157 |
| Sylow | C53 ⋊ C7⋊#1042 |
| Sylow | C52 ⋊ C7⋊#6157 |
| Sylow | C7 ⋊ #19127086 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C7×C53 | C4 |
| prime radical, cosocle | C5×C7×D265 | C2 |
| LCS | G ▷ C52×C7×C53 | |
| UCS | C1 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7420 |
Polycyclic presentation:
2^2,5^2,7,53|a^2=b,c^a=c^2,d^a=d^4,e^a=e^6,f^a=f^23,c^b=c^4,f^b=f^522348 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37100, 74);