Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#22105 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C17 | C24 |
| commutator | C23 | C23×C4×C17 |
| Frattini, cosocle | C22×C4 | C24×C17 |
| socle | C23×C17 | C23×C4 |
| prime radical | C24×C17 | C22×C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C17 ◁ G | |
708 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 2176 |
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)(18,19)(20,21)(23,26)(24,28)(30,31,36,32,35,39,34,38)(33,37,41,40,42,44,43,45);(22,23)(24,27)(25,26)(28,29)(30,32,36,39,35,38,34,31)(33,40,41,44,42,45,43,37);(19,21)(23,26)(27,29)(30,33)(31,37)(32,40)(34,43)(35,42)(36,41)(38,45)(39,44);(22,24,25,28)(23,27,26,29)(30,34,35,36)(31,38,39,32)(33,41,42,43)(37,40,44,45)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 15093);