Finite Group DatabasebetaFinite Group Databasebeta| order | 10644 |
| automorphism | Aut(G) order 9430584 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic2661 |
| unambiguous semidirect product | C3⋊Dic887 |
| unambiguous semidirect product | C887⋊Dic3 |
| derived, Hall | C3×C887 ⋊ C4 |
| Sylow | C887 ⋊ Dic3 |
| Sylow | C3 ⋊ Dic887 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D2661 |
| commutator, hypocenter | C3×C887 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C3×C887 | C2 |
| LCS | G ▷ C3×C887 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,887,2|a^2=d,b^a=b^2,c^a=c^8862664 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic7983, C3⋊Dic2661, C3×Dic2661, … |
| maximal normal subgroup of | C3×Dic2661, Dic5322 |
| maximal quotient of | Dic7983, C3⋊Dic2661, C3×Dic2661, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10644, 4);