Finite Group DatabasebetaFinite Group Databasebeta| order | 14812 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | C7⋊#14523747 |
| Fitting, socle, derived, Hall | C7×C232 ⋊ C4 |
| Sylow | C232 ⋊ Dic7 |
| Sylow | C7 ⋊ #14523747 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C232 | C4 |
| prime radical, cosocle | C7×C23⋊D23 | C2 |
| LCS | G ▷ C7×C232 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 322 |
Polycyclic presentation:
2^2,7,23^2|a^2=b,c^a=c^6,d^a=d^11e^12,e^a=d^9e^12,d^b=d^22,e^b=e^22934 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14812, 23);