Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #22455 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C26 |
| direct product | C17×#22456 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | D4×C22⋊C4 |
| commutator | C2×C4 | C23×C4×C17 |
| Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C2×C17×#577 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C4×C17 ◁ G | |
1336 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)(18,19)(20,28)(21,33,35,25)(22,36)(23,27)(24,31)(26,37)(29,43,46,42)(30,40)(32,39)(34,41,49,48)(38,45,47,44);(18,20,23,32)(19,24,27,40)(21,29,35,46)(22,30,37,31)(25,38,33,47)(26,39,36,28)(34,44,49,45)(41,43,48,42);(18,21)(19,25)(20,29)(22,34)(23,35)(24,38)(26,41)(27,33)(28,42)(30,44)(31,45)(32,46)(36,48)(37,49)(39,43)(40,47);(20,30)(22,37)(24,39)(26,36)(28,40)(29,44)(31,32)(34,49)(38,43)(41,48)(42,47)(45,46)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 15444);