Finite Group DatabasebetaFinite Group Databasebeta| order | 37700 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C13 · Schur multiplier (H2) = C5 |
| direct product | C13×#15668515 |
| derived, Hall | C52×C29 ⋊ C4×C13 |
| Hall | C52×C13×C29 ⋊ C4 |
| Hall | C13×C29 ⋊ #1039 |
| Hall | C52×C13 ⋊ Dic29 |
| Sylow | C29 ⋊ C13×#1039 |
| Sylow | C52 ⋊ C13×Dic29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C13 | C5⋊D145 |
| commutator, hypocenter | C52×C29 | C4×C13 |
| Frattini | C2 | C13×C5⋊D145 |
| Fitting, socle, prime radical | C2×C52×C13×C29 | C2 |
| cosocle | C2×C52×C29 | C2×C13 |
| LCS | G ▷ C52×C29 | |
| UCS | C1 ◁ C2×C13 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 37700 |
9464 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37700, 55);