Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24472 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#24474 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #2410 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C11×#3586 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C4×C11 ◁ G | |
1298 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)(12,13,17,22,18,16,35,21)(14,23,27,25,28,37,26,19)(15,29,33,31,34,39,32,20)(24,36,41,43,42,40,30,38);(12,14)(13,19)(15,30)(16,25)(17,27)(18,28)(20,38)(21,37)(22,23)(24,33)(26,35)(29,36)(31,43)(32,42)(34,41)(39,40);(12,15,18,34)(13,20,16,31)(14,24,28,42)(17,32,35,33)(19,36,25,40)(21,29,22,39)(23,38,37,43)(26,41,27,30);(12,16)(13,18)(14,25)(15,31)(17,21)(19,28)(20,34)(22,35)(23,26)(24,40)(27,37)(29,32)(30,43)(33,39)(36,42)(38,41)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 17462);