Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(5,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C11×C16 · Schur multiplier (H2) = C25 |
| direct product | C11×#33486 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C11 | C24 |
| commutator | C2 | C23×C11×C16 |
| Frattini, cosocle | C2×C8 | C24×C11 |
| socle | C22×C11 | C23×C8 |
| prime radical | C22×D4×C11 | C8 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C11 ◁ G | |
662 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 4 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,18)(15,17)(16,19)(20,21,22,25,23,26,28,31,24,27,29,32,30,33,34,35);(12,14)(13,16)(15,19)(17,18);(14,19)(16,18);(13,17)(16,18)1496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26474);