Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18376 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C24×C4 |
| direct product | C17×#18386 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C17×#1595 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
984 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)(19,24)(20,28)(21,33)(25,39)(26,37)(27,34)(29,43)(30,46)(31,32)(35,48)(38,45)(40,44)(41,49)(42,47);(18,19)(20,29)(21,34)(22,27)(23,26)(24,33)(25,31)(28,40)(30,38)(32,45)(35,49)(36,41)(37,48)(39,42)(43,46)(44,47);(21,35)(24,37)(30,46)(33,48)(34,49)(38,43)(39,44)(42,47);(18,20,23,32)(19,25,26,40)(21,30,35,46)(22,31,36,28)(24,38,37,43)(27,29,41,45)(33,47,48,42)(34,44,49,39)731 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 11374);