Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2883 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#17351 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C22×C22⋊C4 |
| commutator | C22 | C23×C8×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C22×C11×#41 | C4 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C4×D4×C11 ◁ G | |
1278 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)(12,13,14,16,15,17,18,19)(20,21)(22,28,30,25)(23,26)(24,27)(29,34,35,32)(31,33);(20,22,24,30)(21,25,27,28)(23,29,31,35)(26,32,33,34);(20,23)(21,26)(22,29)(24,31)(25,32)(27,33)(28,34)(30,35);(23,31)(26,33)(29,35)(32,34)902 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 10339);