Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33359 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#33360 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | C22×#99 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C2×D4 | C24×C11 |
| prime radical | C11×#3499 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C2×Q8×C11 ◁ C2×C11×2−1+4 ◁ G | |
1188 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,19)(15,20)(16,21,29,18)(17,22)(23,32)(24,33,39,30)(25,34)(26,35)(27,36,41,31)(28,37)(38,43,40,42);(13,18)(16,29)(19,30)(20,31)(21,22)(24,39)(27,41)(32,42)(33,34)(35,43)(36,37)(38,40);(12,14,17,25)(13,19,22,34)(15,26,28,23)(16,24,29,39)(18,30,21,33)(20,35,37,32)(27,40,41,38)(31,43,36,42);(12,15,17,28)(13,20,22,37)(14,23,25,26)(16,27,29,41)(18,31,21,36)(19,32,34,35)(24,38,39,40)(30,42,33,43)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26348);