Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D4×D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C22×C42 |
| direct product | C11×#22613 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C22×D4 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C24×C11 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C4×C11×C22⋊C4 ◁ G | |
778 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,14,15)(16,17)(18,20)(19,21)(22,23)(24,25,29,32,30,33,27,28)(26,34,35,38,36,39,37,31);(16,18,19,22)(17,20,21,23)(24,26)(25,31)(27,35)(28,34)(29,37)(30,36)(32,39)(33,38);(17,21)(20,23)(24,27,30,29)(25,28,33,32)(26,35,36,37)(31,34,38,39);(24,28,27,33,30,32,29,25)(26,31,37,39,36,38,35,34)770 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 15601);