Finite Group DatabasebetaFinite Group Databasebeta| order | 3924 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×Dic109⋊C3 |
| unambiguous semidirect product | Dic109⋊C32 |
| unambiguous semidirect product | (C3×Dic109)⋊C3 |
| derived, Sylow | C109 ⋊ C32×C4 |
| Hall | C3×C109⋊C3 ⋊ C4 |
| Hall | Dic109 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D109⋊C3 |
| commutator, hypocenter | C109 | C32×C4 |
| Frattini | C2 | C3×D109⋊C3 |
| Fitting, socle | C2×C3×C109 | C2×C3 |
| prime radical | C2×C3×C109⋊C3 | C2 |
| cosocle | C2×C109 | C2×C32 |
| LCS | G ▷ C109 | |
| UCS | C1 ◁ C2×C3 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1308 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C5×Dic109⋊C3, C3×Dic545⋊C3, C3×#14546128⋊C3, … |
| maximal normal subgroup of | C3×C5×Dic109⋊C3, C3×C7×Dic109⋊C3 |
| maximal quotient of | C3×C5×Dic109⋊C3, C3×Dic545⋊C3, C3×#14546128⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3924, 22);