Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2812 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C27 |
| direct product | C2×C11×#2843 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C11 | C24 |
| commutator, Frattini, cosocle | C23 | C25×C11 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24×C11 ◁ G | |
1806 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 2816 |
A minimal faithful permutation representation — 5 generators on 37 points:
(1,2)(27,28,29,30,31,32,33,34,35,36,37);(3,4,6,8)(5,7,9,10)(11,12)(13,17)(14,18)(15,16);(5,9)(7,10)(12,16)(14,17)(19,20,22,24)(21,25,26,23);(3,4)(5,7)(6,8)(9,10)(11,13)(12,17)(14,16)(15,18)(19,21,22,26)(20,23,24,25);(3,5)(4,7)(6,9)(8,10)(11,14,15,17)(12,18,16,13)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 29678);