Finite Group DatabasebetaFinite Group Databasebeta| order | 23700 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | (C79⋊C3)⋊#1039 |
| derived, Hall | C52×C79 ⋊ C3×C4 |
| Hall | C79⋊#1039 ⋊ C3 |
| Hall | C52×C79⋊C3 ⋊ C4 |
| Hall | C79⋊C3 ⋊ #1039 |
| Sylow | C79 ⋊ C3×#1039 |
| Sylow | C52 ⋊ (C79⋊C3)⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C5⋊(C5⋊(D79⋊C3)) |
| commutator, hypocenter | C52×C79 | C3×C4 |
| Fitting, socle, cosocle | C2×C52×C79 | C2×C3 |
| prime radical | C2×C52×C79⋊C3 | C2 |
| LCS | G ▷ C52×C79 | |
| UCS | C1 ◁ C2 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7900 |
Polycyclic presentation:
2,3,5^2,79,2|a^2=f,c^a=c^4,d^a=d^4,e^a=e^78,e^b=e^23734 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23700, 45);