Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10440 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C11 · Schur multiplier (H2) = C22 |
| direct product | C11×#10455 |
| 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 | |
376 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 3 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,14,16)(15,17,19,18)(21,26)(22,29)(23,24)(27,34)(28,32)(30,31);(13,16)(17,18)(20,21,25,28)(22,27,31,34)(23,32,24,26)(29,33,30,35);(13,17)(15,19)(16,18)(20,22,24,29,25,31,23,30)(21,27,32,35,28,34,26,33)407 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 3443);