Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33618 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#33618 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | C2×#466 |
| commutator, Frattini, cosocle | C2×C8 | C24×C17 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C4×C17 ◁ C2×C17×#131 ◁ G | |
656 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)(19,25)(20,31)(21,26)(22,23)(27,42)(28,38)(29,40)(30,39)(32,46)(33,36)(34,35)(37,44)(43,49)(45,48);(18,19,26,40,23,30,35,38,24,28,34,39,22,29,21,25)(20,27,41,42,31,44,46,48,33,43,47,49,36,45,32,37);(18,20)(19,27)(21,32)(22,36)(23,31)(24,33)(25,37)(26,41)(28,43)(29,45)(30,44)(34,47)(35,46)(38,48)(39,49)(40,42);(19,28)(25,38)(27,43)(29,30)(37,48)(39,40)(42,49)(44,45)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 26606);