Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24274 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#25487 |
| 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 ◁ C2×C4×Q8×C17 ◁ G | |
722 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)(22,23,26,29)(24,28,25,27)(30,31,36,39,35,40,34,44)(32,41,42,38,33,37,43,45);(18,19)(20,21)(22,24,26,25)(23,27,29,28)(30,32,34,43,35,33,36,42)(31,37,44,38,40,41,39,45);(19,21)(30,33,35,32)(31,38,40,45)(34,43,36,42)(37,39,41,44);(22,25,26,24)(23,28,29,27)(30,34,35,36)(31,39,40,44)(32,42,33,43)(37,38,41,45)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 18475);