Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11×C64 · Schur multiplier (H2) = C2 |
| direct product | C11×C4⋊C64 |
| unambiguous semidirect product | C4⋊(C11×C64) |
| subgroup | G/H | |
|---|---|---|
| center | C2×C11×C32 | C22 |
| commutator | C2 | C2×C11×C64 |
| Frattini, cosocle | C2×C32 | C22×C11 |
| socle, prime radical | C22×C11 | C2×C32 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11×C32 ◁ G | |
74 conjugacy classes of subgroups.
| minimal degree | μ(G) = 79 |
| transitive degree | μt(G) = 2816 |
A minimal faithful permutation representation — 2 generators on 79 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,15)(16,17,18,23,19,24,28,38,20,25,29,39,32,42,48,58,21,26,30,40,33,43,49,59,35,45,51,61,54,64,68,73,22,27,31,41,34,44,50,60,36,46,52,62,55,65,69,74,37,47,53,63,56,66,70,75,57,67,71,76,72,77,78,79);(12,13,14,15)1760 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 531);