Finite Group DatabasebetaFinite Group Databasebeta| order | 7256 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C22⋊D907 |
| Fitting | C22×C907 ⋊ C2 |
| Sylow | C907 ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D907 |
| commutator, socle | C2×C907 | C22 |
| Fitting | C22×C907 | C2 |
| hypercenter | C22 | D907 |
| hypocenter | C907 | D4 |
| LCS | G ▷ C2×C907 ▷ C907 | |
| UCS | C1 ◁ C2 ◁ C22 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2^3,907|b^a=bc,d^b=d^9061817 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D4×D907, C2×C22⋊D907, #28408432, … |
| maximal normal subgroup of | D4×D907, C2×C22⋊D907, #28408432, … |
| maximal quotient of | (C2×D907)⋊C4, C22⋊Dic907, Dic907⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7256, 9);