Finite Group DatabasebetaFinite Group Databasebeta| order | 37100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5×C53 · Schur multiplier (H2) = C1 |
| direct product | C5×C53×C7⋊AGL(1,𝔽5) |
| unambiguous semidirect product | C7⋊(C5×AGL(1,𝔽5)×C53) |
| Fitting, socle, Hall | C52×C7×C53 ⋊ C4 |
| derived | C5×C7 ⋊ C4×C5×C53 |
| Hall | C52×C53 ⋊ Dic7 |
| Hall | C7×C53 ⋊ C5×AGL(1,𝔽5) |
| Hall | C52×C7 ⋊ C4×C53 |
| Sylow | C52 ⋊ Dic7×C53 |
| Sylow | C7 ⋊ C5×AGL(1,𝔽5)×C53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C53 | C7⋊AGL(1,𝔽5) |
| commutator, hypocenter | C5×C7 | C4×C5×C53 |
| Frattini | C1 | G |
| Fitting, socle | C52×C7×C53 | C4 |
| prime radical | C5×C7×D5×C53 | C2 |
| cosocle | C7×D5 | C2×C5×C53 |
| LCS | G ▷ C5×C7 | |
| UCS | C1 ◁ C5×C53 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7420 |
4505 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37100, 64);