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×#1654 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | #120 |
| commutator, Frattini, cosocle | C42 | C24×C11 |
| prime radical | C2×C11×#547 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C2×C42×C11 ◁ G | |
1238 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 29 points:
(1,2)(19,20,21,22,23,24,25,26,27,28,29);(4,8)(5,6)(9,10)(11,12,15,18)(13,16,14,17);(3,4,7,9)(5,8,6,10)(12,16)(13,14)(17,18);(3,5,7,6)(4,8,9,10)(12,17)(13,14)(16,18)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 11484);