Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19014 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#19043 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C11 |
| prime radical | C11×#3558 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
950 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,17,21)(14,22,24,26)(15,19,16,20)(18,25,27,23)(28,29,32,35)(30,36,37,43)(31,39,41,34)(33,40,42,38);(12,14)(13,18)(15,25)(16,23)(17,24)(19,22)(20,26)(21,27)(28,30)(29,33)(31,40)(32,37)(34,43)(35,42)(36,39)(38,41);(12,14)(13,18)(15,23)(16,25)(17,24)(19,26)(20,22)(21,27)(31,41)(34,39)(36,43)(38,40);(12,15,17,16)(13,19,21,20)(14,23,24,25)(18,26,27,22)(30,37)(33,42)(36,43)(38,40)407 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 12031);