Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#17852 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | C22×D4 |
| commutator | C4 | C23×C8×C11 |
| Frattini, cosocle | C42 | C24×C11 |
| socle | C22×C11 | C2×C4×D4 |
| prime radical | C2×C11×AGL(1,ℤ/8) | C4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C11×#431 ◁ G | |
754 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 4 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,15,18,16,14,17,19)(20,21)(22,26)(23,25)(24,28)(27,31)(29,33)(30,32)(34,35);(21,25)(23,31)(26,32)(27,28)(30,35)(33,34);(12,14,15,19,16,13,17,18)(20,22)(21,26)(23,30)(24,29)(25,32)(27,34)(28,33)(31,35);(22,29)(26,33)(30,35)(32,34)968 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 10840);