Finite Group DatabasebetaFinite Group Databasebeta| order | 4788 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #4296⋊Dic7 |
| derived, Hall | C7×C19 ⋊ C4×C9 |
| Hall | C7×#4296 ⋊ C4 |
| Hall | Dic133 ⋊ C9 |
| Hall | #4296 ⋊ Dic7 |
| Sylow | C19 ⋊ C9×Dic7 |
| Sylow | C7 ⋊ #4296⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #4296⋊D7 |
| commutator, hypocenter | C7×C19 | C4×C9 |
| Fitting, socle | C2×C7×C19 | C2×C9 |
| prime radical, cosocle | C2×C7×C19⋊C3 | C2×C3 |
| LCS | G ▷ C7×C19 | |
| UCS | C1 ◁ C2 | |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 30 |
| transitive degree | μt(G) = 532 |
Polycyclic presentation:
2,3^2,7,19,2|a^2=f,b^3=c,d^a=d^6,e^a=e^18,e^b=e^4,e^c=e^7104 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#4296⋊Dic7, #4296⋊Dic35, #4296⋊(C7⋊AGL(1,𝔽5)), … |
| maximal normal subgroup of | C5×#4296⋊Dic7, C7×#4296⋊Dic7 |
| maximal quotient of | C5×#4296⋊Dic7, #4296⋊Dic35, #4296⋊(C7⋊AGL(1,𝔽5)), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4788, 76);