Finite Group DatabasebetaFinite Group Databasebeta| order | 10092 |
| automorphism | Aut(G) order 8194704 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic2523 |
| unambiguous semidirect product | C3⋊Dic841 |
| derived, Hall | C3×C841 ⋊ C4 |
| Sylow | C841 ⋊ Dic3 |
| Sylow | C3 ⋊ Dic841 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D2523 |
| commutator, hypocenter | C3×C841 | C4 |
| Frattini | C2×C29 | D87 |
| Fitting, cosocle | C2×C3×C841 | C2 |
| socle, prime radical | C2×C3×C29 | D29 |
| LCS | G ▷ C3×C841 | |
| UCS | C1 ◁ C2 | |
18 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,29,2,29|a^2=d,c^29=e^28,b^a=b^2,c^a=c^28e,e^a=e^282526 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic7569, C3×Dic2523, C3⋊Dic2523, … |
| maximal normal subgroup of | C3×Dic2523, Dic5046 |
| maximal quotient of | Dic7569, C3×Dic2523, C3⋊Dic2523, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10092, 4);