Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24398 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C26 |
| direct product | C17×#24400 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C22×#41×C17 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C23×C4×C17 ◁ G | |
1322 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 4 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,21)(22,23,26,31,28,33,27,32)(24,29,35,44,36,45,42,49)(25,37,39,48,41,47,40,30)(34,46,38,52,50,53,51,43);(19,21)(22,24)(23,29)(25,38)(26,35)(27,42)(28,36)(30,46)(31,44)(32,49)(33,45)(34,40)(37,52)(39,50)(41,51)(43,47)(48,53);(22,25,28,41)(23,30,33,48)(24,34,36,50)(26,40,27,39)(29,43,45,52)(31,47,32,37)(35,51,42,38)(44,53,49,46);(19,21)731 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 17388);