Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C2×#123×C47 ⋊ C2 |
| Sylow | C47 ⋊ #2710 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D47 |
| commutator, socle | C23×C47 | C24 |
| Fitting | C2×#123×C47 | C2 |
| hypercenter | C2×#123 | D47 |
| hypocenter | C47 | #2710 |
| LCS | G ▷ C23×C47 ▷ C47 | |
| UCS | C1 ◁ C23 ◁ C2×#123 | |
548 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,47|a^2=e,b^2=e,c^2=ef,b^a=be,c^a=cf,d^a=def,c^b=cg,d^b=de,h^b=h^46676 conjugacy classes — view the full character table.
| maximal subgroup of | #26423679, #26423682, #26423762, … |
| maximal normal subgroup of | #26423679, #26423682, #26423762, … |
| maximal quotient of | #26143823, #26143943, #26143971, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 11248);