Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10260 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#10478 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C17 | #121 |
| commutator, Frattini, cosocle | C2×C42 | C23×C17 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C2×C42×C17 ◁ G | |
454 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)(22,23)(24,26)(25,28)(27,29)(30,31,35,39)(32,40,42,45)(33,37,41,36)(34,44,43,38);(18,19)(20,21)(30,32,35,42)(31,36,39,37)(33,43,41,34)(38,45,44,40);(19,21)(23,26)(24,29)(27,28)(30,33,34,32,35,41,43,42)(31,37,38,45,39,36,44,40)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 3466);