Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C17 · Schur multiplier (H2) = C26 |
| direct product | C17×#10771 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | #381 |
| commutator | C23 | C2×C42×C17 |
| Frattini, cosocle | C23×C4 | C23×C17 |
| socle | C2×C17 | C22⋊#95 |
| prime radical | C22×#41×C17 | C22 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C23×C4×C17 ◁ G | |
1164 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)(20,24,29,37)(21,31,32,25)(22,34)(23,26)(27,35)(28,40)(30,44,43,38)(33,39,46,45)(36,41)(42,47)(48,49);(18,20,22,30,23,29,35,43)(19,24,27,38,26,37,34,44)(21,28,33,42,32,41,46,49)(25,36,39,47,31,40,45,48);(18,21)(19,25)(20,28)(22,33)(23,32)(24,36)(26,31)(27,39)(29,41)(30,42)(34,45)(35,46)(37,40)(38,47)(43,49)(44,48)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 3759);