Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4×#120 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C27×C4 |
| direct product | Q8×C11×#124 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C11 |
| prime radical | C22×D4×C11 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ G | |
2326 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 5 generators on 31 points:
(1,2,3,4)(5,8,7,6)(21,22,23,24,25,26,27,28,29,30,31);(1,5,3,7)(2,6,4,8);(10,11)(15,19)(17,20);(9,10,12,11)(13,14,16,18)(15,17,19,20);(9,11,12,10)(13,15)(14,17)(16,19)(18,20)770 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 29536);