Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C17 · Schur multiplier (H2) = C29 |
| direct product | C2×C4×C17×C22⋊Q8 |
| subgroup | G/H | |
|---|---|---|
| center | C23×C4×C17 | C23 |
| commutator | C22 | C24×C4×C17 |
| Frattini, cosocle | C23 | C25×C17 |
| socle | C24×C17 | C24 |
| prime radical | C25×C17 | C23 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C4×C17 ◁ G | |
3854 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 5 generators on 35 points:
(1,2)(19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35);(3,4,5,6);(8,10)(11,12,14,16)(13,17,18,15);(11,13,14,18)(12,15,16,17);(7,8)(9,10)(11,12)(13,15)(14,16)(17,18)1904 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 27018);