Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #8491 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#8502 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #379 |
| commutator | C42 | C22×C4×C17 |
| Frattini, cosocle | C2×C42 | C23×C17 |
| prime radical | C17×#3547 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
672 conjugacy classes of subgroups.
| minimal degree | μ(G) = 65 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 3 generators on 65 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,27,29,23)(21,26)(22,25)(24,28,32,30)(31,33)(34,35,39,44,40,45,38,43)(36,46,50,41,49,56,48,55)(37,42,51,57,52,58,53,59)(47,61,62,65,63,60,64,54);(18,20)(19,23)(21,28)(22,29)(24,26)(25,27)(30,31)(32,33)(34,36)(35,41)(37,47)(38,50)(39,48)(40,49)(42,54)(43,56)(44,46)(45,55)(51,64)(52,63)(53,62)(57,60)(58,65)(59,61);(18,20)(19,24)(21,30)(22,29)(23,26)(25,32)(27,33)(28,31)(34,37,40,52)(35,42,45,58)(36,47,49,63)(38,53,39,51)(41,54,55,65)(43,59,44,57)(46,60,56,61)(48,64,50,62)578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 1490);