Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #22284 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C24×C4 |
| direct product | C11×#22284 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #2328 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C11×#3154 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C4×C11 ◁ G | |
796 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)(14,16)(15,28,32,38)(17,23)(18,24)(19,26)(20,31,39,42)(21,33)(22,35)(25,40,41,36)(27,34)(29,30,37,43);(12,14,17,26,18,27,35,21)(13,19,22,16,24,33,23,34)(15,29,42,25,32,37,31,41)(20,30,28,36,39,43,38,40);(12,15,18,32)(13,20)(14,25)(16,30,34,43)(17,31,35,42)(19,36,33,40)(21,37)(22,38)(23,28)(24,39)(26,29)(27,41);(12,16,17,33,18,34,35,19)(13,21,22,14,24,26,23,27)(15,30,31,40,32,43,42,36)(20,37,38,25,39,29,28,41)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 15272);