Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of AGL(1,ℤ/8) |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8×C11 · Schur multiplier (H2) = C26 |
| direct product | C2×C11×#1479 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C11 | C2×D4 |
| commutator | C4 | C23×C8×C11 |
| Frattini, cosocle | C42 | C24×C11 |
| socle | C23×C11 | C2×C22⋊C4 |
| prime radical | C24×C11 | C22⋊C4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C11 ◁ C22×C42×C11 ◁ G | |
1282 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 37 points:
(1,2)(27,28,29,30,31,32,33,34,35,36,37);(3,4,5,7,6,8,9,10)(11,12)(13,20)(14,18)(15,24)(16,19)(17,22)(21,25)(23,26);(11,13,16,23)(12,17,19,25)(14,22,15,21)(18,26,24,20);(11,14,16,15)(12,18,19,24)(13,21,23,22)(17,20,25,26)968 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 10423);