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×#22459 |
| 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 | |
1312 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)(18,19,23,28,24,29,22,37)(20,30,33,25,34,43,38,42)(21,27,35,44,36,26,39,45)(31,47,32,40,49,41,48,46);(18,20,24,34)(19,25,29,42)(21,31,36,49)(22,38,23,33)(26,40,27,46)(28,43,37,30)(32,39,48,35)(41,44,47,45);(18,21)(19,26)(20,31)(22,35)(23,39)(24,36)(25,40)(27,29)(28,44)(30,41)(32,38)(33,48)(34,49)(37,45)(42,46)(43,47);(18,21)(19,27)(20,32)(22,39)(23,35)(24,36)(25,41)(26,29)(28,44)(30,40)(31,38)(33,49)(34,48)(37,45)(42,47)(43,46)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 15447);