Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D4×AGL(1,ℤ/8) |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C28 |
| direct product | C11×#61460 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C11 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C4×C11×#41 ◁ G | |
1836 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 5 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,16)(17,19)(20,21)(22,26)(23,31)(24,28)(25,29)(27,30)(32,34)(33,35);(12,13)(14,17)(15,16)(18,19)(20,22,25,24)(21,26,29,28)(23,30,32,33)(27,34,35,31);(20,23)(21,27)(22,30)(24,33)(25,32)(26,34)(28,31)(29,35);(13,16)(17,19)(20,22,25,24)(21,26,29,28)(23,30,32,33)(27,34,35,31);(12,14,15,18)(13,17,16,19)(20,22,25,24)(21,28,29,26)(23,30,32,33)(27,31,35,34)605 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 54448);