Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2002 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#23461 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | #120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| socle | C22×C11 | C2×#120 |
| prime radical | C22×C11×#41 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C23×C4×C11 ◁ G | |
1222 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 4 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,15,17)(14,18,19,16)(20,21)(22,26)(23,28)(24,32)(25,29)(27,30)(31,35)(33,34);(12,14,15,19)(13,16,17,18)(20,22)(21,26)(23,30)(24,33)(25,31)(27,28)(29,35)(32,34);(20,22)(21,27)(23,30)(24,33)(25,31)(26,32)(28,35)(29,34);(20,23,25,24)(21,28,29,32)(22,30,31,33)(26,27,35,34)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16449);