Finite Group DatabasebetaFinite Group Databasebeta| order | 7264 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C22⋊C4×C227 ⋊ C2 |
| Sylow | C227 ⋊ #121 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D227 |
| commutator, socle | C22×C227 | C23 |
| Fitting | C22⋊C4×C227 | C2 |
| hypercenter | C22⋊C4 | D227 |
| hypocenter | C227 | #121 |
| LCS | G ▷ C22×C227 ▷ C227 | |
| UCS | C1 ◁ C22 ◁ C22⋊C4 | |
94 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,227|b^2=d,b^a=bd,c^a=ce,f^b=f^226,f^c=f^2261144 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #121×D227, C2×#20300261, #28409540, … |
| maximal normal subgroup of | #121×D227, C2×#20300261, #28409540, … |
| maximal quotient of | #28408891, #28408908, #28408910, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7264, 119);