Finite Group DatabasebetaFinite Group Databasebeta| order | 7264 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C227 ⋊ #125 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D227 |
| commutator, socle | C22×C227 | C23 |
| Fitting | C4⋊C4×C227 | C2 |
| hypercenter | C4⋊C4 | D227 |
| hypocenter | C227 | #125 |
| LCS | G ▷ C22×C227 ▷ C227 | |
| UCS | C1 ◁ C22 ◁ C4⋊C4 | |
56 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,227|a^2=d,b^2=e,c^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 | #28409330, #28409331, #28409334, … |
| maximal normal subgroup of | #28409330, #28409331, #28409334, … |
| maximal quotient of | #28408897, #28408915, #28408919, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7264, 137);