Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of AGL(1,ℤ/8) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8×C11 · Schur multiplier (H2) = C22×C4 |
| direct product | C11×#12615 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C11 | C2×D4 |
| commutator | C4 | C2×C4×C8×C11 |
| Frattini, cosocle | C22×C8 | C23×C11 |
| socle | C22×C11 | C8×D4 |
| prime radical | C2×C11×#41 | C2×C4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C11 ◁ C22×C11×C16 ◁ G | |
418 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,15)(16,17,20,26,21,25,33,40,22,27,34,41,19,23,32,36)(18,24,30,38,31,37,44,46,28,39,42,47,29,35,43,45);(13,15)(17,23,27,25)(18,28)(24,37,39,35)(26,36,41,40)(29,31)(30,42)(38,46,47,45)(43,44);(16,18,20,30,21,31,33,44,22,28,34,42,19,29,32,43)(17,24,26,38,25,37,40,46,27,39,41,47,23,35,36,45)968 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 5603);