Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#9090 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #386 |
| commutator | C2×C4 | C22×C8×C17 |
| Frattini, cosocle | C2×C42 | C23×C17 |
| prime radical | C22×D4×C17 | C2×C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
512 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 3 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,21,24,22,20,23,25)(26,27)(28,31)(29,37,40,35)(30,36)(32,34)(33,39,41,38);(18,20,21,25,22,19,23,24)(26,28,31,27,32,36,30,34)(29,35,38,33,40,37,39,41);(26,29,32,40)(27,33,34,41)(28,35,36,37)(30,39,31,38)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 2078);