Finite Group DatabasebetaFinite Group Databasebeta| order | 1320 |
| isoclinism | isoclinic class of SL(2,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C11 · Schur multiplier (H2) = C1 |
| direct product | C11×SL(2,𝔽5) |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, socle, hypercenter | C2×C11 | A5 |
| commutator, hypocenter | SL(2,𝔽5) | C11 |
| Frattini, cosocle | C2 | C11×A5 |
| LCS | G ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C2×C11 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 264 |
A minimal faithful permutation representation — 2 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,15,19)(14,17,20,16)(18,23,24,28)(21,25,22,26)(27,31,32,35)(29,33,30,34);(12,14,18)(13,16,21)(15,20,24)(17,22,19)(23,27,31)(25,29,33)(26,30,34)(28,32,35)99 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1320, 14);