Finite Group DatabasebetaFinite Group Databasebeta| order | 7836 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#14579726 |
| Fitting, socle, derived, Hall | C3×C653 ⋊ C4 |
| Sylow | C653 ⋊ Dic3 |
| Sylow | C3 ⋊ #14579726 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C653 | C4 |
| LCS | G ▷ C3×C653 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,653|a^2=b,c^a=c^2,d^a=d^504,d^b=d^652495 conjugacy classes — view the full character table.
| maximal subgroup of | C9⋊#14579726, C3×C3⋊#14579726, C3⋊(C3⋊#14579726) |
| maximal normal subgroup of | C3×C3⋊#14579726 |
| maximal quotient of | C9⋊#14579726, C3×C3⋊#14579726, C3⋊(C3⋊#14579726) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7836, 7);