Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3288 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#22465 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | D42 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C2×C11×#578 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C22×C4×C11 ◁ G | |
1312 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 4 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,15)(16,17,21,27,23,19,22,26)(18,28,32,29,33,40,31,24)(20,25,37,42,38,34,36,43)(30,44,35,45,47,41,46,39);(16,18)(17,24)(19,29)(20,35)(21,32)(22,31)(23,33)(25,41)(26,40)(27,28)(30,36)(34,44)(37,47)(38,46)(39,42)(43,45);(13,15)(16,19,23,17)(18,29,33,24)(20,34,38,25)(21,27,22,26)(28,31,40,32)(30,45,47,39)(35,44,46,41)(36,43,37,42);(16,20)(17,25)(18,30)(19,34)(21,37)(22,36)(23,38)(24,39)(26,43)(27,42)(28,44)(29,45)(31,46)(32,35)(33,47)(40,41)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 15453);