Finite Group DatabasebetaFinite Group Databasebeta| order | 6056 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | C2×Dic757 |
| derived, Sylow | C757 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D757 |
| commutator, hypocenter | C757 | C2×C4 |
| Frattini | C2 | C2×D757 |
| Fitting, socle | C22×C757 | C2 |
| LCS | G ▷ C757 | |
| UCS | C1 ◁ C22 | |
16 conjugacy classes of subgroups.
1520 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×Dic757, #27131065, C22⋊Dic757, … |
| maximal normal subgroup of | C4×Dic757, #27131065, C22⋊Dic757, … |
| maximal quotient of | C4×Dic757, C22⋊Dic757, C4⋊Dic757, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6056, 8);