Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3186 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#21969 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | C22×D4 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| socle | C22×C11 | C22×C4⋊C4 |
| prime radical | C24×C11 | C2×Q8 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C22×C42×C11 ◁ G | |
734 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 4 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,18)(15,17)(16,19)(20,21,24,27,25,28,23,33)(22,29,31,34,32,35,30,26);(12,14,15,19)(13,16,17,18);(14,19)(16,18)(20,22,23,30,25,32,24,31)(21,26,27,29,28,34,33,35);(13,17)(16,18)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 14957);