Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of AGL(1,ℤ/8) |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8×C17 · Schur multiplier (H2) = C25 |
| direct product | C8×C17×#137 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C17 | C2×D4 |
| commutator | C4 | C23×C8×C17 |
| Frattini, cosocle | C42 | C24×C17 |
| socle | C22×C17 | C2×C4×D4 |
| prime radical | C2×#41×C17 | C2×C4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C17 ◁ C2×C4×C8×C17 ◁ G | |
714 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 4 generators on 41 points:
(1,2,3,4,5,6,7,8)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41);(9,10)(11,17)(12,20)(13,15)(14,18)(16,22)(19,24)(21,23);(9,11,13,19)(10,14,15,23)(12,21,22,18)(16,24,20,17);(10,15)(14,23)(16,20)(17,24)1496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 10839);