Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C26 |
| direct product | C17×#22465 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | D42 |
| commutator | C2×C4 | C23×C4×C17 |
| Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C2×C17×#578 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C22×C4×C17 ◁ G | |
1312 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 4 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,21)(22,23,27,33,29,25,28,32)(24,34,38,35,39,46,37,30)(26,31,43,48,44,40,42,49)(36,50,41,51,53,47,52,45);(22,24)(23,30)(25,35)(26,41)(27,38)(28,37)(29,39)(31,47)(32,46)(33,34)(36,42)(40,50)(43,53)(44,52)(45,48)(49,51);(19,21)(22,25,29,23)(24,35,39,30)(26,40,44,31)(27,33,28,32)(34,37,46,38)(36,51,53,45)(41,50,52,47)(42,49,43,48);(22,26)(23,31)(24,36)(25,40)(27,43)(28,42)(29,44)(30,45)(32,49)(33,48)(34,50)(35,51)(37,52)(38,41)(39,53)(46,47)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 15453);