Finite Group DatabasebetaFinite Group Databasebeta| order | 7256 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | C2×Dic907 |
| unambiguous semidirect product | (C2×C907)⋊C4 |
| derived, Sylow | C907 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D907 |
| commutator, hypocenter | C907 | C2×C4 |
| Frattini | C2 | C2×D907 |
| Fitting, socle | C22×C907 | C2 |
| LCS | G ▷ C907 | |
| UCS | C1 ◁ C22 | |
16 conjugacy classes of subgroups.
1820 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×Dic907, (C2×D907)⋊C4, C22⋊Dic907, … |
| maximal normal subgroup of | C4×Dic907, (C2×D907)⋊C4, C22⋊Dic907, … |
| maximal quotient of | C4×Dic907, C22⋊Dic907, C4⋊Dic907, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7256, 8);