Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1462 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#8165 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | C2×C22⋊C4 |
| commutator | C23 | C2×C42×C11 |
| Frattini, cosocle | C2×C42 | C23×C11 |
| socle | C22×C11 | C4×C22⋊C4 |
| prime radical | C23×C11 | C2×C42 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C2×C4×C8×C11 ◁ G | |
430 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 3 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,16,18,15,14,17,19)(20,21,23,26)(22,28,29,25)(24,32,31,27)(30,33,35,34);(13,14)(18,19)(20,22,24,30,23,29,31,35)(21,25,27,33,26,28,32,34);(12,14,16,19,15,13,17,18)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 1153);