Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C11×C16 · Schur multiplier (H2) = C2×C42 |
| direct product | C11×#12590 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C8×C11 | C22 |
| commutator | C2 | C2×C4×C11×C16 |
| Frattini, cosocle | C22×C8 | C23×C11 |
| socle, prime radical | C23×C11 | C22×C8 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C8×C11 ◁ G | |
414 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 2816 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,3,4,5,6,7,8,9,10,11)(16,17)(18,21)(19,20)(22,23)(24,25,26,29,27,30,32,35,28,31,33,36,34,37,38,39);(12,13,14,15)(17,20)(21,23);(16,18,19,22)(17,21,20,23)1760 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 5578);