Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33522 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#33686 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C11 |
| prime radical | C11×#3176 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C11×#117 ◁ C11×#405 ◁ G | |
544 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)(14,17)(15,16)(18,19)(21,26)(22,30)(24,35)(25,34)(27,41)(28,44)(31,49)(32,50)(33,48)(36,37)(38,42)(39,46)(43,45)(47,51);(13,16)(17,19)(20,21)(22,27)(23,26)(24,28)(25,29)(30,42)(31,38)(32,43)(33,39)(34,40)(35,46)(36,45)(37,47)(41,49)(44,48)(50,51);(20,22,23,31)(21,27,26,38)(24,36,33,50)(25,37,34,32)(28,45,39,51)(29,47,40,43)(30,48,49,35)(41,46,42,44);(12,14,15,18)(13,17,16,19)(21,26)(27,38)(28,39)(29,40)(41,42)(43,47)(44,46)(45,51)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26674);