Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16×C17 · Schur multiplier (H2) = C22 |
| direct product | C17×#7163 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C8×C17 | D4 |
| commutator | C4 | C4×C16×C17 |
| Frattini, cosocle | C2×C4×C8 | C22×C17 |
| socle | C22×C17 | #336 |
| prime radical | C23×C17 | C4⋊C8 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C8×C17 ◁ C2×C4×C8×C17 ◁ G | |
238 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)(20,22)(21,24)(23,25)(26,27,29,34,31,28,33,37,32,36,30,35,40,39,41,38);(19,22,24,23)(26,28,30,38,31,36,41,34,32,39,29,37,40,27,33,35)1904 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 151);