Finite Group DatabasebetaFinite Group Databasebeta| order | 23700 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C5 |
| direct product | C3×C79⋊#1044 |
| Fitting, socle, Hall | C3×C52×C79 ⋊ C4 |
| derived, Hall | C52×C79 ⋊ C3×C4 |
| Hall | C3×C79 ⋊ #1044 |
| Sylow | C79 ⋊ C3×#1044 |
| Hall | C3×C52 ⋊ Dic79 |
| Sylow | C52 ⋊ C3×Dic79 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C79⋊#1044 |
| commutator, hypocenter | C52×C79 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C79 | C4 |
| prime radical | C3×C5⋊D5×C79 | C2 |
| cosocle | C5⋊D5×C79 | C2×C3 |
| LCS | G ▷ C52×C79 | |
| UCS | C1 ◁ C3 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2370 |
1668 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23700, 120);