Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#36745 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C17 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ G | |
2184 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 5 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,21)(24,28)(27,29)(30,31)(32,33)(34,38)(35,36)(37,41)(39,40)(42,43)(44,45);(23,26)(27,29)(31,36)(32,37)(38,43)(39,44);(18,19,20,21)(22,23)(24,27)(25,26)(28,29)(30,32,35,37)(31,33,36,41)(34,39,42,44)(38,40,43,45);(22,23)(24,27)(25,26)(28,29)(30,33)(31,37)(32,36)(34,40)(35,41)(38,44)(39,43)(42,45);(22,24)(23,27)(25,28)(26,29)(30,34,35,42)(31,38,36,43)(32,39,37,44)(33,40,41,45)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 29733);