Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#22695 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | D42 |
| commutator | C2×C4 | C23×C4×C17 |
| Frattini, cosocle | C22×C4 | C24×C17 |
| socle | C2×C17 | D4×C4⋊C4 |
| prime radical | C2×C17×#135 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C22×C4×C17 ◁ G | |
808 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 4 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,23,30,25,31,24,29)(20,32,36,44,37,48,35,26)(21,38,39,46,40,43,34,27)(22,28,42,47,33,45,41,49);(18,20)(19,26)(21,22)(23,36)(24,35)(25,37)(27,45)(28,46)(29,48)(30,32)(31,44)(33,40)(34,41)(38,49)(39,42)(43,47);(18,21,24,34,25,40,23,39)(19,27,30,38,31,46,29,43)(20,33,35,42,37,22,36,41)(26,28,32,47,44,45,48,49);(18,22)(19,28)(20,34)(21,36)(23,42)(24,41)(25,33)(26,43)(27,32)(29,49)(30,47)(31,45)(35,40)(37,39)(38,44)(46,48)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 15683);