Finite Group DatabasebetaFinite Group Databasebeta| order | 23700 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C52 · Schur multiplier (H2) = C5 |
| direct product | C52×(C79⋊C3)⋊C4 |
| unambiguous semidirect product | (C79⋊C3)⋊(C4×C52) |
| unambiguous semidirect product | Dic79⋊(C3×C52) |
| unambiguous semidirect product | (C5×Dic79)⋊(C3×C5) |
| derived, Sylow | C79 ⋊ C3×C4×C52 |
| Hall | C52×Dic79 ⋊ C3 |
| Hall | C52×C79⋊C3 ⋊ C4 |
| Hall | C52×C79 ⋊ C3×C4 |
| Hall | Dic79 ⋊ C3×C52 |
| Hall | C79⋊C3 ⋊ C4×C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C52 | D79⋊C3 |
| commutator, hypocenter | C79 | C3×C4×C52 |
| Frattini | C2 | C52×D79⋊C3 |
| Fitting, socle | C2×C52×C79 | C2×C3 |
| prime radical | C2×C52×C79⋊C3 | C2 |
| cosocle | C2×C79 | C2×C3×C52 |
| LCS | G ▷ C79 | |
| UCS | C1 ◁ C2×C52 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7900 |
950 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23700, 42);