Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#7882 |
| subgroup | G/H | |
|---|---|---|
| center | C42×C17 | C2×D4 |
| commutator | C4 | C2×C4×C8×C17 |
| Frattini, cosocle | C2×C42 | C23×C17 |
| socle | C22×C17 | C2×#95 |
| prime radical | C24×C17 | C4⋊C4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C42×C17 ◁ C22×C42×C17 ◁ G | |
666 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)(18,19,21,24,23,25,22,20)(26,27)(28,34)(29,37)(30,33)(31,36)(32,38)(35,40)(39,41);(18,20,22,25,23,24,21,19)(26,28)(27,31,33,39)(29,36)(30,35)(32,34,37,40)(38,41);(28,35)(31,39)(34,40)(36,41)1496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 870);