Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C47×#575 ⋊ C2 |
| Sylow | C47 ⋊ #3067 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | #13093996 |
| commutator | C2×C4×C47 | C24 |
| Frattini | C2×C4 | C23×D47 |
| Fitting | C47×#575 | C2 |
| socle | C2×C47 | C2×#121 |
| hypercenter | #575 | D47 |
| hypocenter | C47 | #3067 |
| LCS | G ▷ C2×C4×C47 ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #575 | |
452 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,47|b^2=e,d^2=g,e^2=g,f^2=g,b^a=be,c^a=cf,e^a=eg,f^a=fg,h^b=h^46,f^c=fg538 conjugacy classes — view the full character table.
| maximal subgroup of | #26223213, #26223214, #26223224, … |
| maximal normal subgroup of | #26223213, #26223214, #26223224, … |
| maximal quotient of | #26198517, #26198545, #26198585, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 14227);