Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#61866 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C17 |
| prime radical | C17×#121 | C23 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C17×#533 ◁ G | |
1606 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)(34,35,39,43)(36,40,45,54)(37,47,49,57)(38,50,52,42)(41,51,56,48)(44,58,59,65)(46,62,61,55)(53,63,64,60);(18,20,22,28)(19,23,25,26)(21,29,30,27)(24,32,33,31)(34,36)(35,40)(37,44)(38,46)(39,45)(41,53)(42,55)(43,54)(47,58)(48,60)(49,59)(50,62)(51,63)(52,61)(56,64)(57,65);(34,37,39,49)(35,41,43,56)(36,44,45,59)(38,51,52,48)(40,53,54,64)(42,57,50,47)(46,63,61,60)(55,65,62,58);(18,21,22,30)(19,24,25,33)(20,27,28,29)(23,31,26,32)(36,45)(40,54)(44,59)(46,61)(53,64)(55,62)(58,65)(60,63);(19,25)(23,26)(24,33)(31,32)(36,45)(40,54)(44,59)(46,61)(53,64)(55,62)(58,65)(60,63)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 54854);