Finite Group DatabasebetaFinite Group Databasebeta| order | 912 |
| isoclinism | isoclinic class of D19 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C26 |
| direct product | C23×C3×D19 |
| Fitting, socle | C23×C3×C19 ⋊ C2 |
| derived, Sylow | C19 ⋊ C24×C3 |
| Hall | C3×C19 ⋊ C24 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C3 | D19 |
| commutator, cosocle, hypocenter | C19 | C24×C3 |
| Frattini | C1 | G |
| Fitting, socle | C23×C3×C19 | C2 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C23×C3 | |
268 conjugacy classes of subgroups.
| transitive degree | μt(G) = 456 |
264 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×(C2×D19)⋊Dic3, D19×#217, #14269475, … |
| maximal normal subgroup of | C2×(C2×D19)⋊Dic3, D19×#217, #14269475, … |
| maximal quotient of | C22×C3×Dic38, C22×C3×C4×D19, C22×C3×D76, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(912, 219);