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) = C29 |
| direct product | C11×#61068 |
| 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×D4×C11 ◁ G | |
2772 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 5 generators on 31 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,15)(17,21)(19,27)(22,30)(23,28)(24,31)(25,29);(16,17)(18,24)(19,28)(20,23)(21,27)(22,25)(26,30)(29,31);(13,15);(16,18,20,26)(17,22,23,31)(19,29,27,25)(21,30,28,24);(17,23)(21,28)(22,31)(24,30)605 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 54056);