Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18192 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#18216 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
988 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)(21,33)(22,36)(26,44)(27,40)(28,42)(29,37)(30,43)(34,41)(38,49)(45,46);(18,19)(20,26)(21,34)(22,37)(23,29)(24,30)(25,36)(27,33)(28,39)(31,46)(32,44)(35,41)(38,42)(40,48)(43,49)(45,47);(18,20,24,21)(19,26,30,34)(22,35,38,32)(23,31,39,33)(25,40,43,45)(27,29,46,28)(36,48,49,47)(37,41,42,44);(18,21,24,20)(19,27,30,46)(22,35,38,32)(23,33,39,31)(25,41,43,44)(26,29,34,28)(36,48,49,47)(37,40,42,45)731 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 11204);