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×#18393 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C17×#534 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
910 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)(34,35,39,42)(36,43,46,49)(37,41,38,47)(40,44,48,45);(18,20)(19,23)(21,30)(22,27)(24,32)(25,33)(26,29)(28,31)(34,36)(35,40)(37,45)(38,44)(39,46)(41,49)(42,48)(43,47);(34,35)(36,40)(37,41)(38,47)(39,42)(43,44)(45,49)(46,48);(19,24)(20,27)(25,29)(28,30)(34,37,39,38)(35,41,42,47)(36,44,46,45)(40,43,48,49)731 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 11381);