Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D42 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C17 · Schur multiplier (H2) = C214 |
| direct product | C22×C17×#547 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C17 | C24 |
| commutator, Frattini, cosocle | C22 | C26×C17 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24×C17 ◁ G | |
12230 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 6 generators on 33 points:
(1,2)(17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33);(3,4);(6,8)(9,10,13,14)(11,12,15,16);(10,14)(12,16);(5,6)(7,8)(9,11,13,15)(10,12,14,16);(9,12)(10,15)(11,14)(13,16)1700 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 55687);