Finite Group DatabasebetaFinite Group Databasebeta| order | 23940 |
| automorphism | ? |
| homology | Abelianization (H1) = C7 · Schur multiplier (H2) = C2 |
| direct product | C7×PSL(2,𝔽19) |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C7 | PSL(2,𝔽19) |
| commutator, hypocenter | PSL(2,𝔽19) | C7 |
| Frattini | C1 | G |
| LCS | G ▷ PSL(2,𝔽19) | |
| UCS | C1 ◁ C7 | |
38 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 140 |
A minimal faithful permutation representation — 2 generators on 27 points:
(8,15,13,16,17,23,18,19,9)(11,27,21,12,26,20,14,25,22);(1,2,3,4,5,6,7)(8,20,26)(9,15,11)(10,22,16)(12,23,21)(14,25,17)(18,27,24)84 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23940, 789);