Finite Group DatabasebetaFinite Group Databasebeta| order | 3924 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C22×#11758281 |
| Fitting, socle, Hall | C22×C109 ⋊ C9 |
| derived, Sylow | C109 ⋊ C22×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #11758281 |
| commutator, hypocenter | C109 | C22×C9 |
| Frattini | C1 | G |
| Fitting, socle | C22×C109 | C9 |
| prime radical | C22×C109⋊C3 | C3 |
| cosocle | C109⋊C3 | C22×C3 |
| LCS | G ▷ C109 | |
| UCS | C1 ◁ C22 | |
30 conjugacy classes of subgroups.
| minimal degree | μ(G) = 113 |
| transitive degree | μt(G) = 436 |
84 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D5×#11758281, C22×C5×#11758281, C2×#28351535, … |
| maximal normal subgroup of | C22×C5×#11758281, C22×C7×#11758281 |
| maximal quotient of | C2×D5×#11758281, C22×C5×#11758281, C2×#28351535, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3924, 37);