Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#18126 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | #120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| socle | C22×C17 | C2×#120 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C2×C42×C17 ◁ G | |
1034 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 4 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,23)(20,21)(24,25)(31,37)(38,41);(18,19)(20,23)(21,25)(22,24)(26,27)(28,31)(29,32)(30,33)(34,38)(35,37)(36,39)(40,41);(18,20,22,21)(19,23,24,25)(26,28)(27,31)(29,34)(30,35)(32,38)(33,37)(36,40)(39,41);(26,29,30,36)(27,32,33,39)(28,34,35,40)(31,38,37,41)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 11114);