Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C29 |
| direct product | C17×#61880 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C17 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C4×Q8×C17 ◁ G | |
2302 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)(20,22)(21,24)(23,25)(26,27)(28,36)(29,33)(30,34)(31,35)(32,38)(37,41)(39,40);(26,28,31,38)(27,32,35,36)(29,37,30,39)(33,40,34,41);(19,22)(20,25)(23,24)(26,29,31,30)(27,33,35,34)(28,37,38,39)(32,40,36,41);(26,30,31,29)(27,34,35,33)(28,37,38,39)(32,40,36,41);(27,35)(32,36)(33,34)(40,41)1037 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 54868);