Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12741 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#12741 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #1786 |
| commutator | C2×C8 | C22×C4×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| prime radical | C2×C17×#576 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C4×C17 ◁ C2×C17×#131 ◁ G | |
930 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,29,31,25)(21,24)(22,36)(23,27)(26,33)(28,34)(30,42,47,37)(32,41,46,44)(35,38)(39,48)(40,45,43,49);(19,24)(21,33)(22,34)(25,37)(26,28)(27,38)(29,42)(30,45)(32,46)(35,48)(36,39)(40,41)(43,44)(47,49);(18,20)(19,25)(21,30)(22,32)(23,31)(24,37)(26,40)(27,29)(28,41)(33,45)(34,46)(35,47)(36,44)(38,42)(39,43)(48,49)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 5729);