Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C4×C4⋊C4×C47 ⋊ C2 |
| Sylow | C47 ⋊ #2290 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D47 |
| commutator | C22×C47 | C23×C4 |
| Frattini | C23 | C23×D47 |
| Fitting | C4×C4⋊C4×C47 | C2 |
| socle | C23×C47 | C24 |
| hypercenter | C4×C4⋊C4 | D47 |
| hypocenter | C47 | #2290 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C22×C4 ◁ C4×C4⋊C4 | |
696 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,47|a^2=g,b^2=g,d^2=e,b^a=be,c^a=cf,h^b=h^46,h^c=h^46976 conjugacy classes — view the full character table.
| maximal subgroup of | #26214596, #26214603, #26214633, … |
| maximal normal subgroup of | #26214596, #26214603, #26214633, … |
| maximal quotient of | #26137378, #26137407, #26137419, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 6951);