Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10440 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#10447 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #394 |
| commutator, Frattini, cosocle | C2×C42 | C23×C11 |
| prime radical | C23×C11 | #123 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
408 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 3 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,16)(15,17)(18,19)(20,21,25,29)(22,30,33,45)(23,34,37,27)(24,38,40,28)(26,39,42,32)(31,47,35,46)(36,44,51,49)(41,48,43,50);(13,16)(17,18)(20,22,25,33)(21,26,29,42)(23,35,37,31)(24,39,40,32)(27,43,34,41)(28,45,38,30)(36,48,51,50)(44,46,49,47);(13,17)(15,19)(16,18)(20,23,24,36,25,37,40,51)(21,27,28,44,29,34,38,49)(22,31,32,48,33,35,39,50)(26,41,30,46,42,43,45,47)407 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 3435);