Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12833 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#12833 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #1807 |
| commutator | C2×C8 | C22×C4×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| prime radical | C2×#41×C17 | D4 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C4×C17 ◁ C2×C17×#131 ◁ G | |
358 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)(20,31,35,49)(21,36,38,46)(22,32)(23,28)(24,30)(25,33,39,26)(27,40)(29,42)(34,48,43,37)(41,44)(45,47);(18,20,22,33,23,34,40,46,24,35,41,26,42,43,47,36)(19,25,27,31,29,21,32,37,30,39,45,49,28,38,44,48);(18,21)(19,26)(20,32)(22,37)(23,39)(24,38)(25,42)(27,43)(28,46)(29,36)(30,33)(31,47)(34,45)(35,44)(40,49)(41,48)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 5821);