Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #25446 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#25447 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #2428 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C4×C17 ◁ G | |
892 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)(18,19,23,27,24,28,22,39)(20,29,33,30,34,43,32,25)(21,35,37,41,38,48,36,26)(31,44,46,49,47,40,45,42);(18,20)(19,25,28,30)(21,31)(22,32)(23,33)(24,34)(26,40,41,44)(27,29,39,43)(35,42,48,49)(36,45)(37,46)(38,47);(18,19)(20,30)(21,26)(22,27)(23,39)(24,28)(25,34)(29,33)(31,44)(32,43)(35,36)(37,48)(38,41)(40,47)(42,46)(45,49);(18,21,23,37,24,38,22,36)(19,26,39,48,28,41,27,35)(20,31,33,46,34,47,32,45)(25,40,43,49,30,44,29,42)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 18435);