Finite Group DatabasebetaFinite Group Databasebeta| order | 7260 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting, socle, Hall | C3×C112 ⋊ C2×D5 |
| derived, Hall | C3×#10597245 ⋊ C22 |
| Hall | #10597245 ⋊ C2×D3 |
| Sylow | C112 ⋊ C2×D15 |
| Sylow | C3 ⋊ #11925890⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | C3×#10597245 | C22 |
| Fitting, socle | C3×C112 | C2×D5 |
| LCS | G ▷ C3×#10597245 | |
| UCS | C1 | |
68 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,5,11^2|c^a=c^2,d^a=d^4,e^a=e^5f^8,f^a=e^8f^6,e^b=e^10,f^b=f^10,e^d=e^9f^3,f^d=f^551 conjugacy classes — view the full character table.
| maximal subgroup of | #36344855, C3×#20300024, #36345109, … |
| maximal normal subgroup of | C3×#20300024, #20300024⋊C5, C5×#20300024 |
| maximal quotient of | #36344855, C3×#20300024, #36345109, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7260, 124);