Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#60237 |
| 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 | C2×C17×#532 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ G | |
2168 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)(18,19)(20,24)(21,23)(22,25)(26,27,29,33,30,34,37,41)(28,31,36,38,35,32,39,40);(18,20)(19,22)(21,25)(23,24)(26,28)(27,31)(29,36)(30,35)(32,34)(33,38)(37,39)(40,41);(20,25)(22,24)(26,28)(27,32)(29,36)(30,35)(31,34)(33,40)(37,39)(38,41);(19,23)(22,24);(28,35)(31,32)(36,39)(38,40)1292 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 53225);