Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#11306 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | #124 |
| commutator | C22×C4 | C22×C4×C17 |
| Frattini, cosocle | C23×C4 | C23×C17 |
| socle | C22×C17 | #400 |
| prime radical | C24×C17 | C2×Q8 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C23×C4×C17 ◁ G | |
530 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)(22,23,28,31,27,32,26,33)(24,34,38,44,37,45,36,29)(25,30,41,47,42,48,40,49)(35,46,39,52,51,53,50,43);(18,19)(20,21)(22,24,28,38,27,37,26,36)(23,29,33,45,32,44,31,34)(25,39,40,35,42,50,41,51)(30,46,47,52,48,53,49,43);(19,21)(22,25,26,40,27,42,28,41)(23,30,31,47,32,48,33,49)(24,35,36,50,37,51,38,39)(29,43,34,46,44,52,45,53)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 4294);