Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #25446 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#25448 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #2428 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C17×#3067 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C4×C17 ◁ G | |
860 conjugacy classes of subgroups.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 4 generators on 81 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,25,29,24,31,23,30)(20,32,46,51,36,50,35,26)(21,37,40,27,42,57,41,54)(22,43,47,56,45,55,44,28)(33,52,61,58,38,48,62,66)(34,63,73,75,65,49,64,59)(39,69,70,67,72,53,71,77)(60,79,80,76,68,78,81,74);(18,20,24,36)(19,26)(21,38)(22,34,45,65)(23,35,25,46)(27,52,54,48)(28,49)(29,32)(30,50)(31,51)(33,42)(37,66,57,58)(39,68)(40,62)(41,61)(43,59)(44,64,47,73)(53,76,69,74)(55,75)(56,63)(60,72)(67,79,77,78)(70,81)(71,80);(18,21)(19,27)(20,33)(22,39)(23,40)(24,42)(25,41)(26,48)(28,53)(29,37)(30,57)(31,54)(32,58)(34,60)(35,61)(36,38)(43,67)(44,70)(45,72)(46,62)(47,71)(49,74)(50,66)(51,52)(55,77)(56,69)(59,78)(63,76)(64,80)(65,68)(73,81)(75,79);(18,22,25,47,24,45,23,44)(19,28,30,55,31,56,29,43)(20,34,46,73,36,65,35,64)(21,39,41,71,42,72,40,70)(26,49,50,75,51,63,32,59)(27,53,57,77,54,69,37,67)(33,60,62,81,38,68,61,80)(48,74,66,79,52,76,58,78)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 18436);