Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C26 |
| direct product | C17×#33380 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | C2×D8 |
| commutator | C8 | C23×C4×C17 |
| Frattini, cosocle | C2×C8 | C24×C17 |
| socle | C22×C17 | C22×D8 |
| prime radical | C22×C17×#135 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C23×C4×C17 ◁ C23×C8×C17 ◁ G | |
1170 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)(24,33)(25,31)(26,38)(27,42)(28,30)(29,35)(32,40)(34,50)(36,49)(37,47)(39,45)(41,52)(43,48)(44,51)(46,53);(22,24)(23,29)(25,34)(26,39)(27,43)(28,36)(30,44)(31,45)(32,48)(33,38)(35,40)(37,51)(41,53)(42,46)(47,50)(49,52);(23,30)(29,44)(31,42)(32,47)(33,49)(38,52)(45,46)(48,50);(22,25,28,27)(23,31,30,42)(24,34,36,43)(26,37,41,40)(29,45,44,46)(32,38,47,52)(33,50,49,48)(35,39,51,53)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 26368);