Finite Group DatabasebetaFinite Group Databasebeta| order | 7256 |
| automorphism | Aut(G) order 6573936 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
| dicyclic | Dic1814 |
| unambiguous semidirect product | C907⋊Q8 |
| Sylow | C907 ⋊ Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D907 |
| commutator, socle | C2×C907 | C22 |
| Fitting | C4×C907 | C2 |
| hypercenter | C4 | D907 |
| hypocenter | C907 | Q8 |
| LCS | G ▷ C2×C907 ▷ C907 | |
| UCS | C1 ◁ C2 ◁ C4 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2^3,907|a^2=c,b^2=c,b^a=bc,d^b=d^9061817 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28408421, #28408422, #28408423, … |
| maximal normal subgroup of | #28408421, #28408422, #28408423, … |
| maximal quotient of | Dic907⋊C4, C4⋊Dic907, C2×Dic1814, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7256, 11);