Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33388 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#33388 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | C22×#102 |
| commutator | C8 | C23×C4×C11 |
| Frattini, cosocle | C2×C8 | C24×C11 |
| prime radical | C11×#3584 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C2×C11×#41 ◁ C2×C11×#131 ◁ G | |
1128 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)(13,18,20,32)(15,25)(16,28)(19,31,34,42)(21,26,29,33)(23,38)(24,37)(27,30)(35,39,40,43)(36,41);(12,13)(14,19)(15,26)(16,29)(17,20)(18,30)(21,28)(22,34)(23,39)(24,40)(25,32)(27,33)(31,41)(35,37)(36,43)(38,42);(12,14)(13,19)(15,23)(16,24)(17,22)(18,31)(20,34)(21,35)(25,38)(26,39)(27,36)(28,37)(29,40)(30,41)(32,42)(33,43);(14,22)(19,34)(23,36)(24,37)(31,42)(35,40)(38,41)(39,43)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26376);