Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C11×C16 · Schur multiplier (H2) = C23 |
| direct product | C11×#13553 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C11×C16 | C23 |
| commutator | C22 | C22×C11×C16 |
| Frattini, cosocle | C2×C16 | C23×C11 |
| socle | C22×C11 | C22×C16 |
| prime radical | C24×C11 | C16 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C11×C16 ◁ G | |
330 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,15)(16,17,18,23,19,24,26,35,20,25,27,36,29,37,38,45,21,22,28,32,30,33,39,42,31,34,40,43,41,44,46,47);(13,15);(17,22)(23,32)(24,33)(25,34)(35,42)(36,43)(37,44)(45,47)1232 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 6541);