Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C17 · Schur multiplier (H2) = C26 |
| direct product | C17×#10787 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | #386 |
| commutator | C2×C4 | C2×C42×C17 |
| Frattini, cosocle | C23×C4 | C23×C17 |
| socle | C2×C17 | C22⋊#95 |
| prime radical | C22×#41×C17 | C22 |
| LCS | G ▷ C2×C4 ▷ 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)(18,19,22,28,24,27,23,37)(20,25,32,40,30,41,31,39)(21,33,34,42,35,43,36,26)(29,44,47,38,45,48,46,49);(18,20,23,32,24,30,22,31)(19,25,28,39,27,41,37,40)(21,29,34,46,35,45,36,47)(26,38,43,48,42,49,33,44);(18,21)(19,26)(20,29)(22,36)(23,34)(24,35)(25,38)(27,42)(28,43)(30,45)(31,47)(32,46)(33,37)(39,48)(40,44)(41,49)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 3775);