Finite Group DatabasebetaFinite Group Databasebeta| order | 37100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊#19127056 |
| Fitting, derived, Hall | C7×C25×C53 ⋊ C4 |
| Hall | C25×C53 ⋊ Dic7 |
| Hall | C7×C53 ⋊ #1035 |
| Hall | C7×C25 ⋊ #6157 |
| Sylow | C53 ⋊ C7⋊#1035 |
| Sylow | C25 ⋊ C7⋊#6157 |
| Sylow | C7 ⋊ #19127056 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C7×C25×C53 | C4 |
| Frattini | C5 | C7⋊#11761506 |
| socle | C5×C7×C53 | AGL(1,𝔽5) |
| prime radical, cosocle | C7×D1325 | C2 |
| LCS | G ▷ C7×C25×C53 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9275 |
Polycyclic presentation:
2^2,5,7,53,5|a^2=b,c^5=f,c^a=c^2f,d^a=d^6,e^a=e^23,f^a=f^2,c^b=c^4f^4,e^b=e^52,f^b=f^42327 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37100, 19);