Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #365 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8×C11 · Schur multiplier (H2) = C2×C4 |
| direct product | C11×#7174 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | #106 |
| commutator | C8 | C4×C8×C11 |
| Frattini, cosocle | C2×C4×C8 | C22×C11 |
| socle | C22×C11 | #340 |
| prime radical | C23×C11 | #102 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C2×C42×C11 ◁ C2×C4×C8×C11 ◁ G | |
262 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 2 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,15,18,16,19,14,17)(20,21,24,27,26,30,34,29)(22,25,31,35,28,23,32,33);(13,17,19,18)(20,22,25,27,24,32,35,21,26,28,23,29,34,31,33,30)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 162);