Finite Group DatabasebetaFinite Group Databasebeta| order | 37100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5×C53 · Schur multiplier (H2) = C1 |
| direct product | C5×C53×Dic35 |
| unambiguous semidirect product | C7⋊(C5×Dic5×C53) |
| derived | C5×C7 ⋊ C4×C5×C53 |
| Hall | C52×C7×C53 ⋊ C4 |
| Hall | C52×C53 ⋊ Dic7 |
| Hall | C7×C53 ⋊ C5×Dic5 |
| Hall | C52×C7 ⋊ C4×C53 |
| Sylow | C52 ⋊ Dic7×C53 |
| Sylow | C7 ⋊ C5×Dic5×C53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5×C53 | D35 |
| commutator, hypocenter | C5×C7 | C4×C5×C53 |
| Frattini | C2 | C5×C53×D35 |
| Fitting, socle, prime radical | C2×C52×C7×C53 | C2 |
| cosocle | C2×C5×C7 | C2×C5×C53 |
| LCS | G ▷ C5×C7 | |
| UCS | C1 ◁ C2×C5×C53 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7420 |
10070 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37100, 42);