Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1619 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C2×C11×#1638 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | #120 |
| commutator, Frattini, cosocle | C42 | C24×C11 |
| prime radical | C22×D4×C11 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C2×C42×C11 ◁ G | |
946 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 45 points:
(1,2)(35,36,37,38,39,40,41,42,43,44,45);(3,4,8,11)(5,12,14,17)(6,10,7,15)(9,16,18,13)(19,20,24,28)(21,29,32,33)(22,27,23,26)(25,31,34,30);(3,5)(4,9)(6,13)(7,16)(8,14)(10,17)(11,18)(12,15)(19,21,24,32)(20,25,28,34)(22,31,23,30)(26,33,27,29);(3,6,8,7)(4,10,11,15)(5,13,14,16)(9,17,18,12)(20,26)(22,23)(25,33)(27,28)(29,34)(30,31)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 11481);