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×#24473 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #2410 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C4×C11 ◁ G | |
1314 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)(12,13,18,22,19,16,17,34)(14,23,26,20,28,37,27,25)(15,29,32,31,33,39,35,21)(24,41,42,38,43,36,30,40);(12,14)(13,20)(15,30)(16,25)(17,27)(18,26)(19,28)(21,38)(22,37)(23,34)(24,32)(29,36)(31,40)(33,42)(35,43)(39,41);(12,15)(13,21)(14,24)(16,31)(17,32)(18,35)(19,33)(20,36)(22,39)(23,40)(25,41)(26,30)(27,42)(28,43)(29,34)(37,38);(12,16,19,13)(14,25,28,20)(15,31,33,21)(17,22,18,34)(23,27,37,26)(24,41,43,36)(29,32,39,35)(30,40,42,38)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 17461);