Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C47×#431 ⋊ C2 |
| Sylow | C47 ⋊ C8×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C42 | C22×D47 |
| commutator | C2×C47 | C23×C8 |
| Frattini | C2×C4 | C23×D47 |
| Fitting | C47×#431 | C2 |
| socle | C22×C47 | C23×C4 |
| hypercenter | #431 | D47 |
| hypocenter | C47 | C8×#41 |
| LCS | G ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C42 ◁ #431 | |
456 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,47|a^2=f,c^2=f,d^2=e,f^2=g,b^a=be,h^c=h^461000 conjugacy classes — view the full character table.
| maximal subgroup of | #26106983, #26106985, #26106990, … |
| maximal normal subgroup of | #26106983, #26106985, #26106990, … |
| maximal quotient of | #26214479, #26214484, C4×(C22⋊D47)⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 13466);