Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33764 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#33770 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C11 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C11×#41 ◁ C2×C11×#131 ◁ G | |
576 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,18)(15,17)(16,19)(20,21,24,30)(22,33,35,27)(23,32,26,29)(25,40,39,43)(28,46,47,36)(31,38,49,42)(34,44,37,48)(41,50,51,45);(12,14)(13,16)(15,19)(17,18)(20,22,24,35)(21,27,30,33)(23,37,26,34)(25,36,39,46)(28,40,47,43)(29,48,32,44)(31,45,49,50)(38,51,42,41);(14,19)(16,18)(20,22)(21,28)(23,34)(24,35)(25,41)(26,37)(27,43)(29,45)(30,47)(31,48)(32,50)(33,40)(36,42)(38,46)(39,51)(44,49);(13,17)(16,18)(20,23,24,26)(21,29,30,32)(22,34,35,37)(25,38,39,42)(27,44,33,48)(28,45,47,50)(31,43,49,40)(36,41,46,51)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26758);