Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,ℤ/4) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8×C17 · Schur multiplier (H2) = C42 |
| direct product | C17×#12594 |
| subgroup | G/H | |
|---|---|---|
| center | C42×C17 | C42 |
| commutator | C4 | C2×C4×C8×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| socle | C22×C17 | C2×#97 |
| prime radical | C23×C17 | C2×M16 |
| LCS | G ▷ C4 ▷ C1 | |
| UCS | C1 ◁ C42×C17 ◁ G | |
354 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)(20,23)(21,22)(24,25)(26,27,30,36,31,33,38,40,32,37,39,41,29,35,28,34);(19,22)(23,25)(27,33,37,35)(28,38)(30,39)(34,41,40,36);(18,20,21,24)(19,23,22,25)(26,28,29,39,32,38,31,30)(27,34,35,41,37,40,33,36)1496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 5582);