Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1468 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C27 |
| direct product | C2×C17×#1901 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C2×C22⋊C4 |
| commutator | C23 | C23×C4×C17 |
| Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C25×C17 | C2×C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C24×C4×C17 ◁ G | |
1854 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2)(23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39);(3,4)(5,6)(7,8,10,14,11,13,15,21)(9,12,17,19,16,20,18,22);(7,9,15,17,11,16,10,18)(8,12,14,22,13,20,21,19);(4,6)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 13976);