Finite Group DatabasebetaFinite Group Databasebeta| order | 12340 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C5×C617 ⋊ C4 |
| Sylow | C617 ⋊ AGL(1,𝔽5) |
| Sylow | C5 ⋊ #14578674 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C617 | C4 |
| prime radical, cosocle | D3085 | C2 |
| LCS | G ▷ C5×C617 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,5,617|a^2=b,c^a=c^2,d^a=d^194,c^b=c^4,d^b=d^616775 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#27134635, C3⋊#27134635 |
| maximal normal subgroup of | C3×#27134635 |
| maximal quotient of | C3×#27134635, C3⋊#27134635 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12340, 8);