Finite Group DatabasebetaFinite Group Databasebeta| order | 23700 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C3⋊(C79⋊#1044) |
| unambiguous semidirect product | C79⋊(C3⋊#1044) |
| Fitting, socle, derived, Hall | C3×C52×C79 ⋊ C4 |
| Hall | C52×C79 ⋊ Dic3 |
| Hall | C3×C79 ⋊ #1044 |
| Sylow | C79 ⋊ C3⋊#1044 |
| Hall | C3×C52 ⋊ Dic79 |
| Sylow | C52 ⋊ Dic237 |
| Sylow | C3 ⋊ C79⋊#1044 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C52×C79 | C4 |
| prime radical, cosocle | C3×C5⋊D5×C79 | C2 |
| LCS | G ▷ C3×C52×C79 | |
| UCS | C1 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2370 |
Polycyclic presentation:
2^2,3,5^2,79|a^2=b,c^a=c^2,d^a=d^2,e^a=e^3,f^a=f^78,d^b=d^4,e^b=e^41662 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23700, 146);