Finite Group DatabasebetaFinite Group Databasebeta| order | 9492 |
| automorphism | Aut(G) order 6378624 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic2373 |
| unambiguous semidirect product | C3⋊Dic791 |
| unambiguous semidirect product | C7⋊Dic339 |
| derived, Hall | C3×C7×C113 ⋊ C4 |
| Hall | C7×C113 ⋊ Dic3 |
| Hall | C3×C113 ⋊ Dic7 |
| Sylow | C113 ⋊ Dic21 |
| Hall | C3×C7 ⋊ Dic113 |
| Sylow | C7 ⋊ Dic339 |
| Sylow | C3 ⋊ Dic791 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D2373 |
| commutator, hypocenter | C3×C7×C113 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C3×C7×C113 | C2 |
| LCS | G ▷ C3×C7×C113 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,7,113,2|a^2=e,b^a=b^2,c^a=c^6,d^a=d^1122376 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic7119, C3⋊(ΓL(1,𝔽8)⋊Dic113), C3⋊Dic2373, … |
| maximal normal subgroup of | C3⋊(ΓL(1,𝔽8)⋊Dic113), C3×Dic2373, Dic4746 |
| maximal quotient of | Dic7119, C3⋊Dic2373, C3×Dic2373 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9492, 10);