Finite Group DatabasebetaFinite Group Databasebeta| order | 4788 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #14558781⋊C2 |
| unambiguous semidirect product | #14558785⋊C2 |
| unambiguous semidirect product | #14558787⋊C2 |
| derived, Hall | C7×C19 ⋊ C22×C9 |
| Hall | #11924777 ⋊ C22 |
| Hall | D7×D19 ⋊ C9 |
| Sylow | C19 ⋊ C2×D7⋊C9 |
| Sylow | C7 ⋊ C2×#4294⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #11716322⋊C2 |
| commutator, hypocenter | C7×C19 | C22×C9 |
| Fitting, socle, cosocle | C3×C7×C19 | C22×C3 |
| prime radical | C3×D7×D19 | C3 |
| LCS | G ▷ C7×C19 | |
| UCS | C1 ◁ C3 | |
60 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 1197 |
Polycyclic presentation:
2^2,3,7,19,3|c^3=f,e^a=e^18,d^b=d^6,d^c=d^2,e^c=e^1187 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#14558781⋊C2, #14558781⋊D5, #14558785⋊D5, … |
| maximal normal subgroup of | C5×#14558781⋊C2, C7×#14558781⋊C2 |
| maximal quotient of | C5×#14558781⋊C2, #14558781⋊D5, #14558785⋊D5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4788, 29);