Finite Group DatabasebetaFinite Group Databasebeta| order | 7380 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting, socle, derived, Hall | C32×C5×C41 ⋊ C4 |
| Hall | C32×C41 ⋊ AGL(1,𝔽5) |
| Hall | C5×C41 ⋊ #157 |
| Hall | C32×C5 ⋊ #4223 |
| Sylow | C41 ⋊ #4380 |
| Sylow | C32 ⋊ #11717961 |
| Sylow | C5 ⋊ #13093287 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C5×C41 | C4 |
| LCS | G ▷ C32×C5×C41 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3^2,5,41|a^2=b,c^a=cd,d^a=cd^2,e^a=e^2,f^a=f^32,c^b=c^2,d^b=d^2,e^b=e^4,f^b=f^40465 conjugacy classes — view the full character table.
| maximal subgroup of | #49146756, #20301653⋊C5, C5×#20301653, … |
| maximal normal subgroup of | #20301653⋊C5, C5×#20301653 |
| maximal quotient of | #49146756, C5×#20301653, #49147069, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7380, 131);