Finite Group DatabasebetaFinite Group Databasebeta| order | 7264 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C42×C227 ⋊ C2 |
| Sylow | C227 ⋊ #117 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C2×D227 |
| commutator | C2×C227 | C22×C4 |
| Frattini | C22 | C22×D227 |
| Fitting | C42×C227 | C2 |
| socle | C22×C227 | C23 |
| hypercenter | C42 | D227 |
| hypocenter | C227 | #117 |
| LCS | G ▷ C2×C227 ▷ C227 | |
| UCS | C1 ◁ C2×C4 ◁ C42 | |
76 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,227|a^2=e,c^2=d,b^a=bd,f^b=f^2261828 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28408986, #28408989, #28409047, … |
| maximal normal subgroup of | #28408986, #28408989, #28409047, … |
| maximal quotient of | #28408878, C4×(C2×D227)⋊C4, C4×Dic227⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7264, 103);