Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C22 |
| direct product | C17×#13129 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C17 | #124 |
| commutator | C22×C4 | C22×C4×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| socle | C2×C17 | #1924 |
| prime radical | C2×#41×C17 | C2×C4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C17 ◁ C22×C8×C17 ◁ G | |
306 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)(18,19,23,28,24,29,40,31,22,27,30,34,37,43,45,47)(20,21,26,35,32,36,42,46,33,25,38,39,44,41,48,49);(18,20,30,26,24,32,45,42,22,33,23,38,37,44,40,48)(19,25,28,35,29,41,31,46,27,21,34,39,43,36,47,49);(18,21,22,25)(19,26)(20,31)(23,39,30,35)(24,36,37,41)(27,38)(28,44)(29,42)(32,34)(33,47)(40,49,45,46)(43,48)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6117);