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×#8503 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #379 |
| commutator | C42 | C22×C4×C17 |
| Frattini, cosocle | C2×C42 | C23×C17 |
| prime radical | C17×#3554 | 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)(18,19,22,25,23,27,21,26)(20,28,29,24,30,32,31,33)(34,35)(36,44,47,40)(37,48,50,57)(38,43)(39,42)(41,49,55,51)(45,60)(46,59,64,54)(52,56)(53,61)(58,63)(62,65);(18,20)(19,24)(21,31)(22,29)(23,30)(25,32)(26,28)(27,33)(34,36)(35,40)(37,45)(38,46)(39,47)(41,53)(42,44)(43,54)(48,65)(49,61)(50,62)(51,63)(52,64)(55,58)(56,59)(57,60);(19,25)(21,22)(24,32)(26,27)(28,33)(29,31)(34,37,39,50)(35,41,42,55)(36,45,47,62)(38,51,52,49)(40,53,44,58)(43,57,56,48)(46,63,64,61)(54,60,59,65)578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 1491);