Finite Group DatabasebetaFinite Group Databasebeta| order | 25740 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C13 · Schur multiplier (H2) = C2 |
| direct product | C3×C13×PSL(2,𝔽11) |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C3×C13 | PSL(2,𝔽11) |
| commutator, hypocenter | PSL(2,𝔽11) | C3×C13 |
| Frattini | C1 | G |
| LCS | G ▷ PSL(2,𝔽11) | |
| UCS | C1 ◁ C3×C13 | |
72 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 429 |
A minimal faithful permutation representation — 2 generators on 27 points:
(17,25,21,23,24,20,18,26,22,19,27);(1,2,3)(4,5,6,7,8,9,10,11,12,13,14,15,16)(17,19,22)(18,20,24)(23,25,26)312 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25740, 557);