Finite Group DatabasebetaFinite Group Databasebeta| order | 912 |
| isoclinism | isoclinic class of D3×D19 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C22×D3×D19 |
| unambiguous semidirect product | (D3×C19)⋊C23 |
| unambiguous semidirect product | (C3×D19)⋊C23 |
| unambiguous semidirect product | D57⋊C23 |
| Fitting, socle | C22×C3×C19 ⋊ C22 |
| derived, Hall | C3×C19 ⋊ C24 |
| Sylow | C19 ⋊ C23×D3 |
| Sylow | C3 ⋊ C23×D19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D3×D19 |
| commutator, cosocle, hypocenter | C3×C19 | C24 |
| Frattini | C1 | G |
| Fitting, socle | C22×C3×C19 | C22 |
| LCS | G ▷ C3×C19 | |
| UCS | C1 ◁ C22 | |
268 conjugacy classes of subgroups.
| transitive degree | μt(G) = 228 |
132 conjugacy classes — view the full character table.
| maximal subgroup of | D19×(C2×D3)⋊C4, D3×(C2×D19)⋊C4, #14269390, … |
| maximal normal subgroup of | D19×(C2×D3)⋊C4, D3×(C2×D19)⋊C4, #14269390, … |
| maximal quotient of | C2×Dic6×D19, C2×#11744926, C2×#11744927, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(912, 213);