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×#61403 |
| 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 ◁ C2×C4×Q8×C11 ◁ G | |
1932 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 5 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,17)(18,19)(20,21)(22,25)(23,26)(24,27)(28,31)(29,32)(30,33)(34,35);(12,13,16,17)(14,18,15,19)(20,22,24,30)(21,25,27,33)(23,29,31,35)(26,32,28,34);(12,14,16,15)(13,18,17,19)(21,26)(23,31)(25,32)(27,28)(29,35)(33,34);(12,15,16,14)(13,18,17,19);(21,27)(25,33)(26,28)(32,34)605 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 54391);