Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18376 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#18407 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C17×#3493 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
904 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 1088 |
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)(20,26)(21,29)(22,24)(23,28)(25,31)(27,33)(30,32)(34,35,40,37)(36,43,47,49)(38,42,39,48)(41,45,44,46);(18,20)(19,23)(21,30)(22,27)(24,32)(25,33)(26,29)(28,31)(34,36)(35,41)(37,44)(38,46)(39,45)(40,47)(42,49)(43,48);(34,37,40,35)(36,44,47,41)(38,48,39,42)(43,45,49,46);(19,24)(20,27)(25,29)(28,30)(34,38,40,39)(35,42,37,48)(36,45,47,46)(41,43,44,49)731 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 11395);