Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C2×C4×Q8×C47 ⋊ C2 |
| Sylow | C47 ⋊ #3480 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C23×D47 |
| commutator, socle | C22×C47 | C25 |
| Frattini | C22 | C24×D47 |
| Fitting | C2×C4×Q8×C47 | C2 |
| hypercenter | C2×C4×Q8 | D47 |
| hypocenter | C47 | #3480 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C2×C4 ◁ C2×C4×Q8 | |
1112 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,47|a^2=g,b^2=g,c^2=g,e^2=f,b^a=bf,c^a=cg,d^b=df,h^b=h^46970 conjugacy classes — view the full character table.
| maximal subgroup of | #26108305, #26108309, #26183160, … |
| maximal normal subgroup of | #26108305, #26108309, #26183160, … |
| maximal quotient of | #26375664, Q8×#13093983, #26375711, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 18105);