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×#2007 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | #120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C2×C11×#537 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C23×C4×C11 ◁ G | |
2038 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);(7,8,12,16)(9,17,19,22)(10,15,11,14)(13,20,21,18);(3,4)(5,6)(7,9)(8,13)(10,20)(11,18)(12,19)(14,22)(15,17)(16,21);(4,6)(7,9)(8,13)(10,18)(11,20)(12,19)(14,17)(15,22)(16,21)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16393);