Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#19407 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#121 |
| commutator, Frattini, cosocle | C42 | C24×C17 |
| prime radical | C23×C17 | #121 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
576 conjugacy classes of subgroups.
| minimal degree | μ(G) = 65 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 4 generators on 65 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,23,26)(20,27,30,33)(21,25,22,31)(24,28,32,29)(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);(18,20,22,29,23,30,21,28)(19,24,25,27,26,32,31,33)(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);(18,21,23,22)(19,25,26,31)(20,28,30,29)(24,27,32,33)(36,45)(40,54)(44,59)(46,61)(53,64)(55,62)(58,65)(60,63)833 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 12395);