Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33764 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C23×C4 |
| direct product | C11×#33791 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C11 |
| prime radical | C11×#2186 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C11×#117 ◁ C11×#405 ◁ G | |
574 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)(21,27)(22,31)(23,26)(25,38)(28,42)(30,47)(32,44)(33,50)(34,49)(36,37)(39,40)(41,46)(43,51)(45,48);(12,14,15,19)(13,16,17,18)(20,21)(22,32)(23,35)(24,27)(25,30)(26,29)(28,34)(31,42)(33,43)(36,47)(37,41)(38,46)(39,51)(40,45)(44,49)(48,50);(14,19)(16,18)(20,22)(21,28)(23,33)(24,34)(25,39)(26,40)(27,32)(29,43)(30,48)(31,38)(35,45)(36,49)(37,50)(41,51)(42,47)(44,46);(13,17)(16,18)(20,23,24,26)(21,29,27,35)(22,33,34,40)(25,36,37,38)(28,43,32,45)(30,46,41,47)(31,39,49,50)(42,48,44,51)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26779);