Finite Group DatabasebetaFinite Group Databasebeta| order | 912 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C22 |
| direct product | C19×#239 |
| Fitting | C3×Q8×C19 ⋊ C2 |
| Hall | C3×C19 ⋊ #41 |
| Sylow | C3 ⋊ #41×C19 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C19 | C22×D3 |
| commutator, cosocle | C2×C3 | C23×C19 |
| Frattini | C2 | C22×D3×C19 |
| Fitting | C3×Q8×C19 | C2 |
| socle | C2×C3×C19 | C23 |
| hypercenter | Q8×C19 | D3 |
| hypocenter | C3 | #41×C19 |
| LCS | G ▷ C2×C3 ▷ C3 | |
| UCS | C1 ◁ C2×C19 ◁ Q8×C19 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 456 |
285 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #14269421, #14269427, #14269434, … |
| maximal normal subgroup of | #14269421, #14269427, #14269434, … |
| maximal quotient of | C19×#890, C19×#892, C19×#893, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(912, 190);