Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3198 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C28 |
| direct product | C2×C11×#3243 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C11 |
| prime radical | C2×C11×#121 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C2×C11×#117 ◁ G | |
1742 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 5 generators on 45 points:
(1,2)(35,36,37,38,39,40,41,42,43,44,45);(3,4)(5,11)(6,9)(7,10)(8,13)(12,17)(14,16)(15,18)(19,20)(21,24)(22,25)(23,27)(26,30)(28,32)(29,31)(33,34);(3,5,7,13)(4,8,10,11)(6,14,15,12)(9,17,18,16)(19,21,23,28)(20,24,27,32)(22,29,30,34)(25,31,26,33);(3,6,7,15)(4,9,10,18)(5,12,13,14)(8,16,11,17)(20,25)(22,30)(24,31)(26,27)(29,34)(32,33);(4,10)(8,11)(9,18)(16,17)(21,28)(24,32)(29,34)(31,33)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 53845);