Finite Group DatabasebetaFinite Group Databasebeta| order | 912 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C19⋊GL(2,𝔽3) |
| Fitting | Q8×C19 ⋊ D3 |
| derived | C19×SL(2,𝔽3) ⋊ C2 |
| Sylow | C19 ⋊ GL(2,𝔽3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | A4⋊D19 |
| commutator, cosocle, hypocenter | C19×SL(2,𝔽3) | C2 |
| Fitting | Q8×C19 | D3 |
| socle | C2×C19 | S4 |
| LCS | G ▷ C19×SL(2,𝔽3) | |
| UCS | C1 ◁ C2 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 152 |
Polycyclic presentation:
2,3,19,2^3|d^2=f,e^2=f,b^a=b^2,c^a=c^18,d^a=ef,e^a=df,d^b=e,e^b=def,e^d=ef71 conjugacy classes — view the full character table.
| maximal subgroup of | #14269818, #14269819, #14269822, … |
| maximal normal subgroup of | #14269818, #14269819, #14269822, … |
| maximal quotient of | C19⋊#859, C2×C19⋊GL(2,𝔽3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(912, 118);