Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#21558 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C17 | #121 |
| commutator | C2×C4 | C23×C4×C17 |
| Frattini, cosocle | C22×C4 | C24×C17 |
| socle | C2×C17 | C4×#121 |
| prime radical | C17×#3067 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C17 ◁ C22×C8×C17 ◁ G | |
876 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 4 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,24,29,25,30,23,40)(20,31,22,28,34,45,33,26)(21,35,38,27,39,43,37,44)(32,41,36,46,48,42,47,49);(18,20,23,33,25,34,24,22)(19,26,29,31,30,28,40,45)(21,32,37,47,39,48,38,36)(27,41,43,46,44,42,35,49);(18,21)(19,27)(20,32)(22,36)(23,37)(24,38)(25,39)(26,41)(28,42)(29,43)(30,44)(31,46)(33,47)(34,48)(35,40)(45,49);(18,22,24,34,25,33,23,20)(19,28,29,45,30,26,40,31)(21,36,38,48,39,47,37,32)(27,42,43,49,44,41,35,46)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 14546);