Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #99 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16×C17 · Schur multiplier (H2) = C22 |
| direct product | C17×#7209 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C17 | C22⋊C4 |
| commutator | C22 | C4×C16×C17 |
| Frattini, cosocle | C2×C4×C8 | C22×C17 |
| socle | C22×C17 | #336 |
| prime radical | C23×C17 | C4×C8 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C17 ◁ C2×C4×C8×C17 ◁ G | |
222 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 2 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,20,23,21,22,24,25)(26,27,29,34,31,28,33,37,32,36,30,35,40,39,41,38);(19,22)(20,24)(26,28,30,38,31,36,41,34,32,39,29,37,40,27,33,35)1496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 197);