Finite Group DatabasebetaFinite Group Databasebeta| order | 7460 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C5×C373 ⋊ C4 |
| Sylow | C373 ⋊ AGL(1,𝔽5) |
| Sylow | C5 ⋊ #13093637 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C373 | C4 |
| LCS | G ▷ C5×C373 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,5,373|a^2=b,c^a=c^2,d^a=d^269,c^b=c^4,d^b=d^372470 conjugacy classes — view the full character table.
| maximal subgroup of | #21418652⋊C3, C3×#21418652, C3⋊#21418652, … |
| maximal normal subgroup of | #21418652⋊C3, C3×#21418652, C5×#21418652 |
| maximal quotient of | C3×#21418652, C3⋊#21418652, #49152329, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7460, 9);