Finite Group DatabasebetaFinite Group Databasebeta| order | 10508 |
| automorphism | Aut(G) order 13240080 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic2627 |
| unambiguous semidirect product | C71⋊Dic37 |
| derived, Hall | C37×C71 ⋊ C4 |
| Sylow | C71 ⋊ Dic37 |
| Sylow | C37 ⋊ Dic71 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D2627 |
| commutator, hypocenter | C37×C71 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C37×C71 | C2 |
| LCS | G ▷ C37×C71 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,37,71,2|a^2=d,b^a=b^36,c^a=c^702630 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×Dic2627, Dic7881, C71⋊(Dic37⋊C3), … |
| maximal normal subgroup of | C3×Dic2627, C71⋊(Dic37⋊C3), Dic5254 |
| maximal quotient of | C3×Dic2627, Dic7881, Dic13135 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10508, 4);