Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #20671 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#33427 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | C2×#117 |
| commutator | C2×C4 | C23×C4×C17 |
| Frattini, cosocle | C2×C8 | C24×C17 |
| socle | C2×C17 | C2×#432 |
| prime radical | C24×C17 | M16 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C17×#405 ◁ G | |
524 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)(18,19,21,26,22,27,34,42,23,24,32,37,35,38,47,49)(20,28,30,44,31,36,46,41,29,43,33,48,45,25,39,40);(19,24)(21,32)(25,36)(27,38)(28,43)(30,33)(34,47)(39,46);(18,20)(19,25,24,36)(21,33)(22,31)(23,29)(26,41,37,40)(27,28,38,43)(30,32)(34,39)(35,45)(42,48,49,44)(46,47);(20,29)(25,36)(28,43)(30,33)(31,45)(39,46)(40,41)(44,48)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 26415);