Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13096 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#13098 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #1898 |
| commutator | C22×C4 | C22×C4×C17 |
| Frattini, cosocle | C2×#41 | C23×C17 |
| prime radical | C17×#3010 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C2×C4×C17 ◁ C2×C17×2−1+4 ◁ G | |
640 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,22,30,37)(21,31,34,43)(23,26)(24,27)(25,33,42,39)(28,45)(29,36,38,47)(32,46)(35,48)(40,44)(41,49);(18,20,22,27,24,30,37,19)(21,28,35,42,34,41,32,25)(23,38,36,26,40,29,47,44)(31,39,46,49,43,33,48,45);(18,21)(19,25)(20,28)(22,35)(23,39)(24,34)(26,43)(27,42)(29,48)(30,41)(31,44)(32,37)(33,40)(36,49)(38,46)(45,47)578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6086);