Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #22455 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#22459 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | D4×C22⋊C4 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C2×C11×#577 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C4×C11 ◁ G | |
1312 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,17,22,18,23,16,31)(14,24,27,19,28,37,32,36)(15,21,29,38,30,20,33,39)(25,41,26,34,43,35,42,40);(12,14,18,28)(13,19,23,36)(15,25,30,43)(16,32,17,27)(20,34,21,40)(22,37,31,24)(26,33,42,29)(35,38,41,39);(12,15)(13,20)(14,25)(16,29)(17,33)(18,30)(19,34)(21,23)(22,38)(24,35)(26,32)(27,42)(28,43)(31,39)(36,40)(37,41);(12,15)(13,21)(14,26)(16,33)(17,29)(18,30)(19,35)(20,23)(22,38)(24,34)(25,32)(27,43)(28,42)(31,39)(36,41)(37,40)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 15447);