Finite Group DatabasebetaFinite Group Databasebeta| order | 3924 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D9×D109 |
| unambiguous semidirect product | (D9×C109)⋊C2 |
| unambiguous semidirect product | (C9×D109)⋊C2 |
| unambiguous semidirect product | D981⋊C2 |
| Fitting, derived, Hall | C9×C109 ⋊ C22 |
| Sylow | C109 ⋊ C2×D9 |
| Sylow | C9 ⋊ C2×D109 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C9×C109 | C22 |
| Frattini | C3 | D3×D109 |
| socle | C3×C109 | C2×D3 |
| LCS | G ▷ C9×C109 | |
| UCS | C1 | |
30 conjugacy classes of subgroups.
| minimal degree | μ(G) = 118 |
| transitive degree | μt(G) = 981 |
336 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D9×D109, D45×D109, D9×D545, … |
| maximal normal subgroup of | C5×D9×D109, C7×D9×D109 |
| maximal quotient of | C5×D9×D109, D45×D109, D9×D545, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3924, 12);