Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#60559 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C17 |
| socle | C22×C17 | C23×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C22×C42×C17 ◁ G | |
2170 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 5 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,23)(21,22)(24,25)(26,27)(28,31)(29,32)(30,33)(34,37)(35,38)(36,39)(40,41);(19,22)(23,25)(26,28,30,36)(27,31,33,39)(29,35,37,41)(32,38,34,40);(27,32)(29,37)(31,38)(33,34)(35,41)(39,40);(18,20,21,24)(19,23,22,25);(27,33)(31,39)(32,34)(38,40)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 53547);