Finite Group DatabasebetaFinite Group Databasebeta| order | 10492 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C43⋊#6923 |
| Fitting, socle, derived, Hall | C43×C61 ⋊ C4 |
| Sylow | C61 ⋊ Dic43 |
| Sylow | C43 ⋊ #6923 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C43×C61 | C4 |
| prime radical, cosocle | C43×D61 | C2 |
| LCS | G ▷ C43×C61 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,43,61|a^2=b,c^a=c^42,d^a=d^50,d^b=d^60691 conjugacy classes — view the full character table.
| maximal subgroup of | #44538351, #44538352, (C43⋊C3)⋊#6923, … |
| maximal normal subgroup of | #44538351, #44538352, (C43⋊C3)⋊#6923, … |
| maximal quotient of | C3×C43⋊#6923, C3⋊(C43⋊#6923) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10492, 7);