Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#9040 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | #120 |
| commutator | C22×C4 | C22×C4×C17 |
| Frattini, cosocle | C23×C4 | C23×C17 |
| prime radical | C24×C17 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C23×C4×C17 ◁ G | |
750 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 1088 |
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)(19,21)(22,23)(24,28,29,26)(25,27)(30,31,34,38,36,39,35,44)(32,40,41,45,33,42,43,37);(18,19,20,21)(22,23)(24,26)(25,27)(28,29)(30,32,36,33)(31,37,39,45)(34,43,35,41)(38,42,44,40);(22,24)(23,26)(25,29)(27,28)(30,33,36,32)(31,37,39,45)(34,43,35,41)(38,40,44,42)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 2028);