Finite Group DatabasebetaFinite Group Databasebeta| order | 23700 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C79⋊#64480 |
| Fitting, socle, Hall | C52×C79 ⋊ Dic3 |
| derived, Hall | C52⋊C3×C79 ⋊ C4 |
| Sylow | C79 ⋊ #64480 |
| Hall | C52⋊C3 ⋊ Dic79 |
| Sylow | C52 ⋊ Dic237 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | C52⋊C3×C79 | C4 |
| Fitting, socle | C52×C79 | Dic3 |
| prime radical, cosocle | C79×(C5⋊D5)⋊C3 | C2 |
| LCS | G ▷ C52⋊C3×C79 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1185 |
Polycyclic presentation:
2^2,3,79,5^2|a^2=b,c^a=c^2,d^a=d^78,e^a=e^3,f^a=ef^2,e^b=e^4,f^b=f^4,e^c=ef,f^c=e^2f^3398 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23700, 74);