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×#20998 |
| 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 | |
1704 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)(12,13,17,22,18,23,16,21)(14,24,27,35,28,34,26,19)(15,29,30,20,32,36,31,37)(25,33,39,42,41,43,40,38);(12,14)(13,19,23,35)(15,25)(16,26)(17,27)(18,28)(20,33,37,43)(21,34,22,24)(29,38,36,42)(30,39)(31,40)(32,41);(12,15)(13,20)(14,25)(16,30)(17,31)(18,32)(19,33)(21,36)(22,29)(23,37)(24,38)(26,39)(27,40)(28,41)(34,42)(35,43);(12,16,18,17)(13,21,23,22)(14,26,28,27)(15,30,32,31)(19,34,35,24)(20,36,37,29)(25,39,41,40)(33,42,43,38)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 13986);