Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C11 · Schur multiplier (H2) = C29 |
| direct product | C22×C11×#432 |
| subgroup | G/H | |
|---|---|---|
| center | C23×C4×C11 | C23 |
| commutator | C22 | C24×C4×C11 |
| Frattini, cosocle | C2×C4 | C25×C11 |
| socle | C24×C11 | C22×C4 |
| prime radical | C25×C11 | C2×C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C4×C11 ◁ G | |
2830 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)(21,22,23,24,25,26,27,28,29,30,31);(3,4);(5,6)(7,10)(8,9)(11,12)(13,14,15,18,16,17,19,20);(6,9)(10,12);(5,7,8,11)(6,10,9,12)(14,17)(18,20)1232 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 53103);