Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60771 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#60884 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C17 |
| prime radical | C2×#41×C17 | C23 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C4×#41×C17 ◁ G | |
1622 conjugacy classes of subgroups.
| minimal degree | μ(G) = 65 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 5 generators on 65 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,26)(21,24)(22,25)(23,28)(27,32)(29,31)(30,33)(34,35,39,44)(36,40,45,53)(37,42,48,56)(38,41,50,43)(46,52,58,63)(47,54,59,51)(49,55,61,57)(60,64,65,62);(18,20,22,28)(19,23,25,26)(21,29,30,27)(24,32,33,31)(34,36)(35,40)(37,46)(38,47)(39,45)(41,54)(42,52)(43,51)(44,53)(48,58)(49,60)(50,59)(55,64)(56,63)(57,62)(61,65);(18,21,22,30)(19,24,25,33)(20,27,28,29)(23,31,26,32)(35,41)(36,45)(38,50)(40,51)(42,55)(43,44)(46,58)(49,61)(52,62)(53,54)(56,57)(63,64);(19,25)(23,26)(24,33)(31,32)(34,37)(35,42)(36,46)(38,49)(39,48)(40,52)(41,55)(43,57)(44,56)(45,58)(47,60)(50,61)(51,62)(53,63)(54,64)(59,65);(37,48)(42,56)(46,58)(49,61)(52,63)(55,57)(60,65)(62,64)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 53872);