Finite Group DatabasebetaFinite Group Databasebeta| order | 23700 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C79 · Schur multiplier (H2) = C1 |
| direct product | C79×C3⋊#1042 |
| unambiguous semidirect product | C3⋊(C79×#1042) |
| Fitting, socle, Hall | C3×C52×C79 ⋊ C4 |
| derived, Hall | C3×C52 ⋊ C4×C79 |
| Hall | C52×C79 ⋊ Dic3 |
| Hall | C3×C79 ⋊ #1042 |
| Sylow | C52 ⋊ Dic3×C79 |
| Sylow | C3 ⋊ C79×#1042 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C79 | C3⋊#1042 |
| commutator, hypocenter | C3×C52 | C4×C79 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C79 | C4 |
| prime radical | C3×C5×D5×C79 | C2 |
| cosocle | C3×C5×D5 | C2×C79 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 ◁ C79 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4740 |
2607 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23700, 129);