Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#33604 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C17 |
| socle | C22×C17 | C22×D8 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C23×C4×C17 ◁ C23×C8×C17 ◁ G | |
690 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)(25,30)(26,40)(27,42)(28,32)(29,37)(31,34)(35,46)(36,47)(38,52)(39,45)(41,53)(43,50)(44,51)(48,49);(22,24,34,49,27,38,41,50,28,35,39,51,25,36,26,37)(23,29,40,47,30,44,45,46,32,43,53,52,42,48,31,33);(19,21)(24,35)(29,43)(33,46)(36,38)(37,50)(44,48)(47,52)(49,51);(22,25,28,27)(23,30,32,42)(24,36,35,38)(26,39,41,34)(29,44,43,48)(31,40,45,53)(33,47,46,52)(37,51,50,49)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 26592);