Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33605 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#33750 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C11 |
| prime radical | C11×#2218 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ C2×C4×C8×C11 ◁ G | |
516 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)(20,21)(22,27)(23,33)(24,38)(25,40)(26,30)(28,37)(29,35)(31,45)(32,44)(34,47)(36,48)(39,51)(41,46)(42,49)(43,50);(13,16)(17,19)(20,22,26,25)(21,27,30,40)(23,34,36,31)(24,32,39,35)(28,42,43,41)(29,38,44,51)(33,47,48,45)(37,49,50,46);(20,23,35,49,25,34,39,50,26,36,32,46,22,31,24,37)(21,28,38,45,27,41,44,48,30,43,51,47,40,42,29,33);(12,14,15,18)(13,17,16,19)(23,36)(28,43)(31,34)(33,48)(37,50)(41,42)(45,47)(46,49)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26738);