Finite Group DatabasebetaFinite Group Databasebeta| order | 7264 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C227 ⋊ SD32 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #16813869 |
| commutator | C8×C227 | C22 |
| Frattini | C8 | C2×D227 |
| Fitting | D8×C227 | C2 |
| socle | C2×C227 | D8 |
| hypercenter | D8 | D227 |
| hypocenter | C227 | SD32 |
| LCS | G ▷ C8×C227 ▷ C4×C227 ▷ C2×C227 ▷ C227 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ D8 | |
26 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,227|a^2=e,c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,f^a=f^226,c^b=cd,d^b=de802 conjugacy classes — view the full character table.
| maximal subgroup of | SD32×D227, C2×#20300232, #28409461, … |
| maximal normal subgroup of | SD32×D227, C2×#20300232, #28409461, … |
| maximal quotient of | #28408833, #28408835, #28408859, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7264, 90);