Finite Group DatabasebetaFinite Group Databasebeta| order | 7260 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, Hall | C5×C112 ⋊ Dic3 |
| derived, Hall | C5×C112⋊C3 ⋊ C4 |
| Hall | C112⋊C3 ⋊ AGL(1,𝔽5) |
| Sylow | C112 ⋊ ΓL(1,𝔽16) |
| Sylow | C5 ⋊ #13089712 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | C5×C112⋊C3 | C4 |
| Fitting, socle | C5×C112 | Dic3 |
| LCS | G ▷ C5×C112⋊C3 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,5,11^2|a^2=b,c^a=c^2,d^a=d^2,e^a=e^2f^10,f^a=e^3f^9,d^b=d^4,e^c=e^2f^10,f^c=e^7f^8119 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#20300037, C3⋊#20300037, #49137115, … |
| maximal normal subgroup of | C3×#20300037, #20300037⋊C5, C5×#20300037 |
| maximal quotient of | #36344868, C3×#20300037, C3⋊#20300037, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7260, 137);