Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2048 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#11273 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | #394 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| socle | C2×C11 | #1442 |
| prime radical | C24×C11 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C23×C4×C11 ◁ G | |
576 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,18,23,33)(15,25)(16,29)(17,20)(19,27)(21,30)(22,36,26,41)(24,40,39,32)(28,42)(31,43,34,38)(35,37);(12,14,16,24,17,23,30,39)(13,18,21,32,20,33,29,40)(15,26,27,43,28,22,37,38)(19,34,25,41,35,31,42,36);(12,15)(13,19,20,35)(14,22,23,26)(16,27)(17,28)(18,31)(21,25,29,42)(24,38,39,43)(30,37)(32,36)(33,34)(40,41)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4261);