Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#12996 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #447 |
| commutator | C2×C8 | C22×C4×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| prime radical | C2×C17×#472 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C22×C4×C17 ◁ C2×C17×#131 ◁ G | |
512 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)(19,21)(22,23,25,31,26,32,41,46,28,34,42,45,27,33,39,29)(24,35,36,52,43,30,47,48,38,51,40,44,37,49,53,50);(18,19,20,21)(23,29)(25,39)(26,27)(30,44)(31,33)(32,45)(34,46)(35,50)(36,53)(37,43)(40,47)(41,42)(48,51)(49,52);(22,24)(23,30)(25,40)(26,43)(27,37)(28,38)(29,44)(31,50)(32,51)(33,35)(34,49)(36,42)(39,47)(41,53)(45,48)(46,52)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 5984);