Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#60273 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | C25 |
| commutator | C22 | C24×C4×C17 |
| Frattini, cosocle | C2×C4 | C25×C17 |
| socle | C22×C17 | C24×C4 |
| prime radical | C17×#3475 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ G | |
1826 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 5 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,22)(20,24)(26,27,30,33,29,31,37,38)(28,34,36,41,35,32,39,40);(18,19)(20,23)(21,22)(24,25)(27,31)(32,34)(33,38)(40,41);(19,22)(23,25)(27,31)(32,34)(33,38)(40,41);(18,20,21,24)(19,23,22,25)(26,28,29,35)(27,32,31,34)(30,36,37,39)(33,40,38,41);(28,35)(32,34)(36,39)(40,41)1292 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 53261);