Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2002 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C27 |
| direct product | C2×C11×#2005 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | #120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C22×C11×#41 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C23×C4×C11 ◁ G | |
1998 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 4 generators on 33 points:
(1,2)(23,24,25,26,27,28,29,30,31,32,33);(3,4)(5,6)(7,8)(9,17)(10,14)(11,20)(12,16)(13,18)(15,21)(19,22);(7,9,12,10)(8,13,16,22)(11,19,21,18)(14,20,17,15);(4,6)(7,10,12,9)(8,14,16,17)(11,18,21,19)(13,15,22,20)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16386);