Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9495 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#9511 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #386 |
| commutator | C24 | C22×C4×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| prime radical | C11×#2404 | C2 |
| LCS | G ▷ C24 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G | |
812 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 3 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,16,18,19)(15,17)(20,21,24,28,25,27,34,22)(23,30,32,35,31,26,33,29);(12,14)(13,16,17,19)(15,18)(20,22,24,27,25,28,34,21)(23,29,33,30,31,35,32,26);(20,23)(21,26)(22,29)(24,33)(25,31)(27,30)(28,35)(32,34)407 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 2499);