Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18376 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24×C4 |
| direct product | C11×#18386 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C11×#1595 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
984 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)(13,18)(14,22)(15,27)(19,33)(20,31)(21,28)(23,37)(24,40)(25,26)(29,42)(32,39)(34,38)(35,43)(36,41);(12,13)(14,23)(15,28)(16,21)(17,20)(18,27)(19,25)(22,34)(24,32)(26,39)(29,43)(30,35)(31,42)(33,36)(37,40)(38,41);(15,29)(18,31)(24,40)(27,42)(28,43)(32,37)(33,38)(36,41);(12,14,17,26)(13,19,20,34)(15,24,29,40)(16,25,30,22)(18,32,31,37)(21,23,35,39)(27,41,42,36)(28,38,43,33)473 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 11374);