Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17577 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#17678 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C22×C22⋊C4 |
| commutator | C2×C4 | C23×C4×C17 |
| Frattini, cosocle | C42 | C24×C17 |
| prime radical | C17×#3444 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C22×C42×C17 ◁ G | |
976 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 1088 |
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)(18,19,22,25,23,26,21,30)(20,27,28,32,29,24,31,33)(34,35)(36,44,46,48)(37,42)(38,41)(39,43)(40,45,49,47);(18,20)(19,24)(21,28)(22,31)(23,29)(25,32)(26,27)(30,33)(34,36)(35,40)(37,45)(38,47)(39,46)(41,48)(42,44)(43,49);(34,37,39,38)(35,41,43,42)(36,45,46,47)(40,48,49,44);(18,21,23,22)(19,25,26,30)(20,28,29,31)(24,32,27,33)(34,37,39,38)(35,42,43,41)(36,45,46,47)(40,44,49,48)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 10666);