Finite Group DatabasebetaFinite Group Databasebeta| order | 7264 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C227 ⋊ M32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C2×D227 |
| commutator, socle | C2×C227 | C2×C8 |
| Fitting | C2×C8×C227 | C2 |
| hypercenter | C2×C8 | D227 |
| hypocenter | C227 | M32 |
| LCS | G ▷ C2×C227 ▷ C227 | |
| UCS | C1 ◁ C8 ◁ C2×C8 | |
26 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,227|a^2=c,c^2=d,d^2=e,b^a=be,f^a=f^2261828 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28408809, #28408810, #28408813, … |
| maximal normal subgroup of | #28408809, #28408810, #28408813, … |
| maximal quotient of | #28408808, C22⋊(C227⋊C16), C4⋊(C227⋊C16), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7264, 86);