Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18992 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#18996 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C11 |
| prime radical | C11×#3529 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
948 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 4 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,16)(14,18)(17,19)(20,21,26,31)(22,32,36,42)(23,37,39,45)(24,30,25,29)(27,34,43,35)(28,40,44,38)(33,41,49,51)(46,48,50,47);(14,18)(16,19)(20,22)(21,27)(23,33)(24,34)(25,35)(26,36)(28,41)(29,42)(30,32)(31,43)(37,50)(38,47)(39,49)(40,48)(44,51)(45,46);(12,13)(14,19)(15,17)(16,18)(20,23)(21,28)(22,33)(24,38)(25,40)(26,39)(27,41)(29,37)(30,45)(31,44)(32,46)(34,47)(35,48)(36,49)(42,50)(43,51);(20,24,26,25)(21,29,31,30)(22,34,36,35)(23,38,39,40)(27,42,43,32)(28,37,44,45)(33,47,49,48)(41,50,51,46)374 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 11984);