Finite Group DatabasebetaFinite Group Databasebeta| order | 9844 |
| automorphism | Aut(G) order 11478104 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic2461 |
| unambiguous semidirect product | C23⋊Dic107 |
| unambiguous semidirect product | C107⋊Dic23 |
| derived, Hall | C23×C107 ⋊ C4 |
| Sylow | C107 ⋊ Dic23 |
| Sylow | C23 ⋊ Dic107 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D2461 |
| commutator, hypocenter | C23×C107 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C23×C107 | C2 |
| LCS | G ▷ C23×C107 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,23,107,2|a^2=d,b^a=b^22,c^a=c^1062464 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×Dic2461, Dic7383, Dic4922 |
| maximal normal subgroup of | C3×Dic2461, Dic4922 |
| maximal quotient of | C3×Dic2461, Dic7383 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9844, 4);