Finite Group DatabasebetaFinite Group Databasebeta| order | 7264 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C22⋊C4×C227 ⋊ C2 |
| Sylow | C227 ⋊ #123 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D227 |
| commutator, socle | C22×C227 | C23 |
| Fitting | C22⋊C4×C227 | C2 |
| hypercenter | C22⋊C4 | D227 |
| hypocenter | C227 | #123 |
| LCS | G ▷ C22×C227 ▷ C227 | |
| UCS | C1 ◁ C22 ◁ C22⋊C4 | |
78 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,227|c^2=d,b^a=bd,c^a=ce,f^a=f^226,f^c=f^2261144 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28409223, #123×D227, C2×#20300272, … |
| maximal normal subgroup of | #28409223, #123×D227, C2×#20300272, … |
| maximal quotient of | #28408893, #28408907, #28408909, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7264, 130);