Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#60882 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C17 |
| prime radical | C17×#3512 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C4×#41×C17 ◁ G | |
1650 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)(36,41)(37,43)(38,44)(39,53)(40,45)(42,50)(46,55)(47,56)(48,63)(49,57)(51,58)(52,59)(54,60)(61,64)(62,65);(18,20,22,28)(19,23,25,26)(21,29,30,27)(24,32,33,31)(34,36,40,49)(35,41,45,57)(37,46,51,61)(38,47,39,48)(42,54,59,65)(43,55,58,64)(44,56,53,63)(50,60,52,62);(18,21,22,30)(19,24,25,33)(20,27,28,29)(23,31,26,32)(34,37)(35,42)(36,46)(38,50)(39,52)(40,51)(41,54)(43,53)(44,58)(45,59)(47,60)(48,62)(49,61)(55,63)(56,64)(57,65);(19,25)(23,26)(24,33)(31,32)(34,37)(35,43)(36,46)(38,52)(39,50)(40,51)(41,55)(42,53)(44,59)(45,58)(47,62)(48,60)(49,61)(54,63)(56,65)(57,64);(34,38,40,39)(35,44,45,53)(36,47,49,48)(37,50,51,52)(41,56,57,63)(42,58,59,43)(46,60,61,62)(54,64,65,55)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 53870);