Finite Group DatabasebetaFinite Group Databasebeta| order | 23700 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C79⋊#64470 |
| derived, Hall | C52⋊C3×C79 ⋊ C4 |
| Hall | C52×C79 ⋊ Dic3 |
| Sylow | C79 ⋊ #64470 |
| Hall | C52⋊C3 ⋊ Dic79 |
| Sylow | C52 ⋊ Dic237 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C79⋊#3874 |
| commutator, hypocenter | C52⋊C3×C79 | C4 |
| Fitting, socle | C2×C52×C79 | D3 |
| prime radical, cosocle | C2×C52⋊C3×C79 | C2 |
| LCS | G ▷ C52⋊C3×C79 | |
| UCS | C1 ◁ C2 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4740 |
Polycyclic presentation:
2,3,79,5^2,2|a^2=f,b^a=b^2,c^a=c^78,d^a=d^2e,e^a=d^2e^3,d^b=d^2e^4,e^b=d^2e^2884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23700, 48);