Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61569 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C28 |
| direct product | C11×#61705 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C11 |
| prime radical | C22×D4×C11 | D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C4×D4×C11 ◁ G | |
1742 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 5 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,20)(15,18)(16,19)(17,22)(21,26)(23,25)(24,27)(28,29,32,36)(30,33,37,41)(31,34,39,35)(38,42,43,40);(12,14)(13,17)(15,21)(16,22)(18,24)(19,20)(23,27)(25,26)(28,30)(29,33)(31,38)(32,37)(34,42)(35,40)(36,41)(39,43);(12,15,16,23)(13,18,19,25)(14,21,22,27)(17,24,20,26)(29,34)(30,37)(31,39)(33,40)(35,36)(41,42);(14,22)(17,20)(21,27)(24,26);(13,19)(17,20)(18,25)(24,26)539 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 54693);