Finite Group DatabasebetaFinite Group Databasebeta| order | 2016 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived | C3×SL(2,𝔽7) ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊SO(3,𝔽7) |
| commutator, cosocle, hypocenter | C3×SL(2,𝔽7) | C2 |
| Fitting, socle | C2×C3 | SO(3,𝔽7) |
| LCS | G ▷ C3×SL(2,𝔽7) | |
| UCS | C1 ◁ C2 | |
76 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 2 generators on 19 points:
(1,2)(4,9)(5,8)(6,19)(7,14)(10,17)(11,18)(12,16);(1,2,3)(4,11,10,7,15,17,16)(5,6,14,18,8,9,13)27 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#72275713, D3×#10621462 |
| maximal normal subgroup of | C3×#72275713, D3×#10621462 |
| maximal quotient of | C3×#72275713 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((1,2)(4,9)(5,8)(6,19)(7,14)(10,17)(11,18)(12,16), (1,2,3)(4,11,10,7,15,17,16)(5,6,14,18,8,9,13));