Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D42 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C13 · Schur multiplier (H2) = C214 |
| direct product | C22×C13×#550 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C13 | C24 |
| commutator, Frattini, cosocle | C22 | C26×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24×C13 ◁ G | |
12918 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 6 generators on 29 points:
(1,2)(17,18,19,20,21,22,23,24,25,26,27,28,29);(3,4);(6,8)(10,11)(14,15);(9,10,13,11)(12,15,16,14);(5,6)(7,8)(9,11,13,10)(12,15,16,14);(9,12,13,16)(10,14,11,15)1300 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 55688);