Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3003 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C24×C4 |
| direct product | C11×#21061 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C22×D4 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C24×C11 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G | |
1126 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,14)(16,17,19,18)(20,21)(22,30)(23,29)(24,26)(25,28)(27,31)(32,35)(33,34);(12,13,15,14)(16,18,19,17)(21,26)(27,34)(28,29)(30,35);(12,14,15,13)(20,22,24,32)(21,27,26,34)(23,31,25,33)(28,30,29,35);(20,23,24,25)(21,28,26,29)(22,31,32,33)(27,30,34,35)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 14049);