Finite Group DatabasebetaFinite Group Databasebeta| order | 912 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | Q8×D57 |
| Fitting | C3×Q8×C19 ⋊ C2 |
| Hall | C3×C19 ⋊ C2×Q8 |
| Sylow | C19 ⋊ D3×Q8 |
| Sylow | C3 ⋊ Q8×D19 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D57 |
| commutator, socle, cosocle | C2×C3×C19 | C23 |
| Fitting | C3×Q8×C19 | C2 |
| prime radical | C2×D57 | C22 |
| hypercenter | Q8 | D57 |
| hypocenter | C3×C19 | C2×Q8 |
| LCS | G ▷ C2×C3×C19 ▷ C3×C19 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 456 |
150 conjugacy classes — view the full character table.
| maximal subgroup of | #14269422, #14269428, #14269439, … |
| maximal normal subgroup of | #14269422, #14269428, #14269439, … |
| maximal quotient of | #14269725, #14269726, #14269727, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(912, 199);