Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#36720 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C17 |
| prime radical | C23×D4×C17 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ G | |
2450 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)(18,19,20,21)(24,28)(27,29)(30,31)(32,36)(33,35)(34,41)(37,42)(38,40)(39,44)(43,45);(23,26)(27,29)(31,33)(36,38)(37,41)(43,44);(18,19)(20,21)(22,23)(24,27)(25,26)(28,29)(30,32,35,40)(31,36,33,38)(34,39,42,45)(37,43,41,44);(22,23)(24,27)(25,26)(28,29)(30,33,35,31)(32,38,40,36)(34,41,42,37)(39,44,45,43);(22,24)(23,27)(25,28)(26,29)(30,34)(31,37)(32,39)(33,41)(35,42)(36,43)(38,44)(40,45)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 29708);