Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1902 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C27 |
| direct product | C11×#20995 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | #386 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| socle | C2×C11 | C2×#386 |
| prime radical | C2×C11×#575 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C23×C4×C11 ◁ G | |
1664 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)(15,28,31,37)(16,21)(17,22)(18,23)(19,26)(20,29,36,30)(25,39,42,33)(27,34)(32,35)(38,41,43,40);(12,14,16,26,18,27,17,32)(13,19,22,24,23,35,21,34)(15,25,29,40,31,42,30,41)(20,33,37,38,36,39,28,43);(12,15)(13,20)(14,25)(16,29)(17,30)(18,31)(19,33)(21,28)(22,37)(23,36)(24,38)(26,40)(27,42)(32,41)(34,43)(35,39);(12,16,18,17)(13,21,23,22)(14,26,27,32)(15,29,31,30)(19,34,35,24)(20,28,36,37)(25,40,42,41)(33,43,39,38)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 13983);