Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C47 ⋊ #2360 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D47 |
| commutator | C22×C47 | C23×C4 |
| Fitting | C47×#385 | C2 |
| socle | C23×C47 | C24 |
| hypercenter | #385 | D47 |
| hypocenter | C47 | #2360 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C23 ◁ #385 | |
620 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,47|a^2=g,b^2=g,d^2=e,b^a=be,c^a=cf,d^b=de,h^d=h^46694 conjugacy classes — view the full character table.
| maximal subgroup of | D47×#2360, C2×#20246388, #26375837, … |
| maximal normal subgroup of | D47×#2360, C2×#20246388, #26375837, … |
| maximal quotient of | #26137690, #26137785, #26137789, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 7510);