Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C8×C11 · Schur multiplier (H2) = C29 |
| direct product | C23×C11×M32 |
| subgroup | G/H | |
|---|---|---|
| center | C23×C8×C11 | C22 |
| commutator | C2 | C24×C8×C11 |
| Frattini, cosocle | C8 | C25×C11 |
| socle | C24×C11 | C2×C8 |
| prime radical | C25×C11 | C8 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C8×C11 ◁ G | |
2334 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 5 generators on 33 points:
(1,2)(23,24,25,26,27,28,29,30,31,32,33);(3,4);(5,6);(7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22);(8,16)(10,18)(12,20)(14,22)1760 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 55609);