Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17597 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#17621 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C22×C22⋊C4 |
| commutator | C2×C4 | C23×C4×C17 |
| Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C22×D4×C17 | D4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C4×D4×C17 ◁ G | |
990 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 4 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,24,26,39)(20,29)(21,33)(25,41,42,47)(27,40,28,34)(30,32)(35,37)(38,44,49,43);(18,19,22,27)(20,25,29,43)(21,34,33,39)(23,28,36,26)(24,37,40,35)(30,42,32,44)(31,47,45,49)(38,46,41,48);(18,20)(19,25)(21,31)(22,29)(23,32)(24,38)(26,42)(27,43)(28,44)(30,36)(33,45)(34,47)(35,48)(37,46)(39,49)(40,41);(20,30)(25,42)(29,32)(31,46)(38,49)(41,47)(43,44)(45,48)833 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 10609);