Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23860 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#25552 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C2×C17×#555 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C2×C4×D4×C17 ◁ G | |
1166 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)(19,21)(22,23)(24,28)(25,27)(26,29)(30,31)(32,37)(33,42)(34,38)(35,43)(36,39)(40,44)(41,45);(22,24,25,29)(23,26,27,28)(30,32,36,41)(31,37,39,45)(33,34,40,35)(38,44,43,42);(18,19,20,21)(30,33,35,32,36,40,34,41)(31,37,38,42,39,45,43,44);(23,27)(26,28)(30,34,36,35)(31,38,39,43)(32,40,41,33)(37,44,45,42)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 18540);