Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C26 |
| direct product | C17×#24411 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #2410 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C17×#3586 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C4×C17 ◁ G | |
1294 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)(20,30,34,25)(21,35)(22,40,42,27)(23,28)(24,29)(26,38)(31,56,59,46)(32,47)(33,54,44,48)(36,63,62,49)(37,64,66,50)(39,55)(41,68,71,52)(43,53)(45,51)(57,60)(58,78)(61,73)(65,81)(67,77,70,75)(69,76)(72,79)(74,80);(18,20,23,34)(19,25,28,30)(21,36,38,62)(22,32,42,60)(24,44,43,33)(26,49,35,63)(27,47,40,57)(29,54,53,48)(31,45,59,39)(37,65,66,80)(41,69,71,61)(46,55,56,51)(50,74,64,81)(52,76,68,73)(58,70,79,67)(72,77,78,75);(18,21)(19,26)(20,31)(22,37)(23,38)(24,45)(25,46)(27,50)(28,35)(29,55)(30,56)(32,58)(33,62)(34,59)(36,44)(39,43)(40,64)(41,70)(42,66)(47,72)(48,63)(49,54)(51,53)(52,77)(57,78)(60,79)(61,80)(65,69)(67,71)(68,75)(73,81)(74,76);(18,22)(19,27)(20,32)(21,37)(23,42)(24,41)(25,47)(26,50)(28,40)(29,52)(30,57)(31,58)(33,61)(34,60)(35,64)(36,65)(38,66)(39,67)(43,71)(44,69)(45,70)(46,72)(48,73)(49,74)(51,75)(53,68)(54,76)(55,77)(56,78)(59,79)(62,80)(63,81)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 17399);