Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #560 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C11 · Schur multiplier (H2) = C213 |
| direct product | C2×C11×#3531 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C11 | C24 |
| commutator, Frattini, cosocle | C22 | C26×C11 |
| socle | C23×C11 | C25 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C11 ◁ G | |
6554 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 6 generators on 45 points:
(1,2)(35,36,37,38,39,40,41,42,43,44,45);(3,4)(5,11)(6,10)(7,9)(8,12)(13,17)(14,16)(15,18)(19,20)(21,24)(22,29)(23,26)(25,31)(27,34)(28,33)(30,32);(3,5)(4,8)(6,13)(7,12)(9,11)(10,15)(14,18)(16,17)(19,21,23,28)(20,24,26,33)(22,30,31,27)(25,34,29,32);(5,12)(8,11)(13,18)(15,17)(19,22,23,31)(20,25,26,29)(21,27,28,30)(24,32,33,34);(4,9)(5,12)(10,16)(13,18)(20,26)(24,33)(25,29)(32,34);(3,6,7,14)(4,10,9,16)(5,13,12,18)(8,15,11,17)836 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 55681);