Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C17 · Schur multiplier (H2) = C2×C42 |
| direct product | C17×#8025 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C2×C22⋊C4 |
| commutator | C2×C4 | C2×C42×C17 |
| Frattini, cosocle | C23×C4 | C23×C17 |
| prime radical | C24×C17 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C22×C42×C17 ◁ G | |
654 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 3 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)(24,30)(25,33)(26,29)(27,32)(28,34)(31,36)(35,37)(38,39)(40,46)(41,44)(42,45)(43,48)(47,52)(49,51)(50,53);(22,24)(23,27,29,35)(25,32)(26,31)(28,30,33,36)(34,37)(38,40)(39,43,45,46)(41,49)(42,48)(44,52,53,51)(47,50);(24,31)(27,35)(30,36)(32,37)(38,41,42,50)(39,44,45,53)(40,47,48,49)(43,51,46,52)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 1013);