Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#13064 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | C2×D8 |
| commutator | C2×C8 | C22×C4×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| socle | C22×C17 | C2×#102 |
| prime radical | C17×#3050 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C23×C4×C17 ◁ C23×C8×C17 ◁ G | |
488 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)(22,23,26,31,28,32,27,42)(24,33,36,49,34,47,37,52)(25,38,39,44,41,53,40,30)(29,43,46,50,45,51,48,35);(22,24,25,35,26,36,39,43,28,34,41,50,27,37,40,51)(23,29,44,47,42,48,38,49,32,45,30,33,31,46,53,52);(19,21)(24,34)(29,45)(33,47)(35,50)(36,37)(43,51)(46,48)(49,52)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6052);