Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D42 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C11 · Schur multiplier (H2) = C213 |
| direct product | C22×C11×#556 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C11 | C24 |
| commutator, Frattini, cosocle | C22 | C26×C11 |
| prime radical | C23×D4×C11 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24×C11 ◁ G | |
7846 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 6 generators on 31 points:
(1,2)(21,22,23,24,25,26,27,28,29,30,31);(3,4);(5,6)(7,9)(8,11)(10,12)(15,19)(17,20);(5,7,10,8)(6,11,12,9)(13,14,16,18)(15,17,19,20);(5,8,10,7)(6,11,12,9)(13,15)(14,17)(16,19)(18,20);(5,9,10,11)(6,7,12,8)1100 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 55694);