Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#26371 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C17 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C4×C4⋊C4×C17 ◁ G | |
780 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)(22,23,26,28)(24,27,25,29)(30,31)(32,37)(33,41)(34,36)(35,39)(38,40)(42,44)(43,45);(18,19)(20,21)(22,24,26,25)(23,27,28,29)(31,36)(32,34)(37,39)(38,41)(40,43)(44,45);(19,21)(22,25,26,24)(23,27,28,29)(30,32,35,34)(31,37,39,36)(33,40,42,43)(38,44,45,41);(30,33,35,42)(31,38,39,45)(32,40,34,43)(36,41,37,44)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 19359);