Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18414 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#18424 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G | |
1020 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)(14,24)(15,18)(16,22)(17,31)(19,23)(20,26)(21,33)(25,34)(27,37)(28,40)(29,42)(30,35)(32,36)(38,43)(39,41);(12,14,18,28)(13,20,15,25)(16,26,17,34)(19,29,36,27)(21,37,30,42)(22,40,31,24)(23,39,32,38)(33,41,35,43);(12,15,18,13)(14,25,28,20)(16,21,17,30)(19,32,36,23)(22,35,31,33)(24,41,40,43)(26,37,34,42)(27,39,29,38);(12,16,18,17)(13,21,15,30)(14,26,28,34)(19,33,36,35)(20,37,25,42)(22,32,31,23)(24,39,40,38)(27,43,29,41)407 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 11412);