Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C26 |
| direct product | C17×#20852 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | C22×D4 |
| commutator | C2×C4 | C23×C4×C17 |
| Frattini, cosocle | C22×C4 | C24×C17 |
| socle | C22×C17 | C22×C4⋊C4 |
| prime radical | C22×#41×C17 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C22×#41×C17 ◁ G | |
1314 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)(22,23,27,31,28,32,26,40)(24,33,35,29,36,43,41,44)(25,30,39,46,37,45,38,50)(34,47,49,42,48,53,51,52);(22,24,27,35,28,36,26,41)(23,29,31,43,32,44,40,33)(25,34,39,49,37,48,38,51)(30,42,46,53,45,52,50,47);(19,21)(22,25)(23,30)(24,34)(26,38)(27,39)(28,37)(29,42)(31,46)(32,45)(33,47)(35,49)(36,48)(40,50)(41,51)(43,53)(44,52);(25,37)(30,45)(34,48)(38,39)(42,52)(46,50)(47,53)(49,51)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 13840);