Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18346 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#18354 |
| 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 ◁ C23×C4×C17 ◁ G | |
1022 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)(20,29)(21,31)(22,34)(26,39)(27,35)(28,41)(30,44)(32,48)(33,36)(37,46)(40,42)(43,49)(45,47);(18,19)(20,26)(21,32)(22,35)(23,28)(24,27)(25,34)(29,42)(30,45)(31,47)(33,40)(36,48)(37,49)(38,43)(39,44)(41,46);(18,20,24,21)(19,26,27,32)(22,36,34,44)(23,29,38,31)(25,39,35,48)(28,42,43,47)(30,46,33,37)(40,49,45,41);(18,21,24,20)(19,26,27,32)(22,33,34,30)(23,31,38,29)(25,40,35,45)(28,42,43,47)(36,37,44,46)(39,49,48,41)578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 11342);