Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C23×C4 |
| direct product | C17×#22814 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C17 | C22×D4 |
| commutator | C2×C4 | C23×C4×C17 |
| Frattini, cosocle | C22×C4 | C24×C17 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C4×C4⋊C4×C17 ◁ G | |
770 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 4352 |
A minimal faithful permutation representation — 4 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,20,21)(22,23)(24,27)(25,29)(26,28)(30,31,35,33,36,39,34,38)(32,40,42,37,43,44,41,45);(22,24,26,25)(23,27,28,29)(30,32,36,43)(31,37,39,45)(33,40,38,44)(34,42,35,41);(22,25,26,24)(23,27,28,29);(30,33,35,39,36,38,34,31)(32,37,42,44,43,45,41,40)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 15802);