Finite Group DatabasebetaFinite Group Databasebeta| order | 6056 |
| automorphism | Aut(G) order 4578336 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
| dicyclic | Dic1514 |
| unambiguous semidirect product | C757⋊Q8 |
| Sylow | C757 ⋊ Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D757 |
| commutator, socle | C2×C757 | C22 |
| Fitting | C4×C757 | C2 |
| hypercenter | C4 | D757 |
| hypocenter | C757 | Q8 |
| LCS | G ▷ C2×C757 ▷ C757 | |
| UCS | C1 ◁ C2 ◁ C4 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2^3,757|a^2=c,b^2=c,b^a=bc,d^b=d^7561517 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27131076, #27131077, #27131078, … |
| maximal normal subgroup of | #27131076, #27131077, #27131078, … |
| maximal quotient of | #27131067, C4⋊Dic757, C2×Dic1514, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6056, 11);