Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C22×C4 |
| direct product | C17×#9742 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C17 | #121 |
| commutator | C42 | C22×C4×C17 |
| Frattini, cosocle | C2×C42 | C23×C17 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C2×C42×C17 ◁ G | |
506 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 4352 |
A minimal faithful permutation representation — 3 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,21)(22,23,24,27,25,28,29,26)(30,31)(32,40)(33,36)(34,43)(35,39)(37,41)(38,44)(42,45);(18,19,20,21)(23,26)(24,29)(27,28)(30,32,34,33,35,41,44,42)(31,36,38,40,39,45,43,37);(30,33,34,41,35,42,44,32)(31,37,38,36,39,40,43,45)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 2730);