Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2846 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C27 |
| direct product | C2×C11×#2863 |
| 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 | |
2142 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);(3,4,8,7)(5,10,6,9)(11,12,15,18)(13,16,17,14)(21,25)(23,26);(3,5,8,6)(4,9,7,10)(11,13,15,17)(12,16,18,14)(19,20,22,24)(21,23,25,26);(3,6,8,5)(4,10,7,9)(11,14,15,16)(12,17,18,13);(3,7,8,4)(5,10,6,9)(11,12)(13,16)(14,17)(15,18)(19,21)(20,23)(22,25)(24,26)968 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 29621);