Finite Group DatabasebetaFinite Group Databasebeta| order | 912 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C3×C19 ⋊ D8 |
| Sylow | C19 ⋊ D24 |
| Sylow | C3 ⋊ #64525 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #90697 |
| commutator, Fitting, cosocle | C3×C4×C19 | C22 |
| Frattini, hypercenter | C4 | D3×D19 |
| socle | C2×C3×C19 | D4 |
| hypocenter | C3×C19 | D8 |
| LCS | G ▷ C3×C4×C19 ▷ C2×C3×C19 ▷ C3×C19 | |
| UCS | C1 ◁ C2 ◁ C4 | |
44 conjugacy classes of subgroups.
| minimal degree | μ(G) = 30 |
| transitive degree | μt(G) = 456 |
Polycyclic presentation:
2^4,3,19|a^2=c,c^2=d,b^a=bc,f^a=f^18,c^b=cd,e^b=e^296 conjugacy classes — view the full character table.
| maximal subgroup of | D19×D24, #14269166, #14269167, … |
| maximal normal subgroup of | D19×D24, #14269166, #14269167, … |
| maximal quotient of | #14268829, #14268834, #14268835, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(912, 31);