Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#61435 |
| 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 ◁ C4×#41×C17 ◁ G | |
1852 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 2176 |
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)(19,22)(23,25)(26,27,31,34)(28,32,30,38)(29,36,37,40)(33,39,41,35);(18,19)(20,23)(21,22)(24,25)(26,28,31,30)(27,32,34,38)(29,35,37,39)(33,40,41,36);(26,29)(27,33)(28,35)(30,39)(31,37)(32,40)(34,41)(36,38);(19,22)(23,25)(26,28,31,30)(27,32,34,38)(29,35,37,39)(33,40,41,36);(18,20,21,24)(19,23,22,25)(26,28,31,30)(27,32,34,38)(29,35,37,39)(33,40,41,36)1190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 54423);