Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #509 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C17 · Schur multiplier (H2) = C22 |
| direct product | C17×#12043 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | C2×D8 |
| commutator | C8 | C22×C8×C17 |
| Frattini, cosocle | C4×C8 | C23×C17 |
| socle | C22×C17 | C4×D8 |
| prime radical | C2×D8×C17 | C2×C4 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C4×C8×C17 ◁ C82×C17 ◁ G | |
238 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 3 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,21,24,22,20,23,25)(26,27)(28,31)(29,38)(30,32)(33,35)(34,36)(37,39)(40,41);(27,31)(28,35)(29,36)(32,39)(33,34)(37,41)(38,40);(18,20,21,25,22,19,23,24)(27,32)(31,39)(33,40)(34,38)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 5031);