Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C17 · Schur multiplier (H2) = C26 |
| direct product | C17×#10756 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | #386 |
| 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 | |
1192 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)(18,19,22,27,23,26,34,40)(20,24,30,37,29,36,33,41)(21,25,32,38,31,39,45,49)(28,42,44,48,43,35,46,47);(18,20)(19,24,26,36)(21,28)(22,33)(23,29)(25,35,39,42)(27,41,40,37)(30,34)(31,43)(32,46)(38,48,49,47)(44,45);(18,21)(19,25)(20,28)(22,32)(23,31)(24,35)(26,39)(27,38)(29,43)(30,44)(33,46)(34,45)(36,42)(37,47)(40,49)(41,48)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 3744);