Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1999 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C26 |
| direct product | C17×#23504 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C17 | C2×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| socle | C23×C17 | C22×D4 |
| prime radical | C2×C17×#532 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C17 ◁ C22×C42×C17 ◁ G | |
1522 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 4 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,21)(23,24)(26,27)(28,36)(29,33)(30,34)(31,35)(32,39)(37,40)(38,41);(22,23)(24,25)(26,27)(28,37)(29,33)(30,34)(31,35)(32,38)(36,40)(39,41);(19,21)(22,24,25,23)(26,28)(27,32)(29,38)(30,39)(31,40)(33,36)(34,37)(35,41);(26,29,31,30)(27,33,35,34)(28,38,40,39)(32,36,41,37)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 16492);