Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C47 ⋊ #3078 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D188 |
| commutator | C2×C4×C47 | C24 |
| Frattini | C2×C4 | C23×D47 |
| Fitting | C47×#423 | C2 |
| socle | C22×C47 | C22×D4 |
| hypercenter | #423 | D47 |
| hypocenter | C47 | #3078 |
| LCS | G ▷ C2×C4×C47 ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ #423 | |
376 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 145 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,47|a^2=e,b^2=e,c^2=g,f^2=g,b^a=be,c^a=cf,d^a=dg,f^a=fg,h^a=h^46,f^c=fg,h^c=h^46676 conjugacy classes — view the full character table.
| maximal subgroup of | #26112191, #26112193, #26112205, … |
| maximal normal subgroup of | #26112191, #26112193, #26112205, … |
| maximal quotient of | #26215767, #26217247, #26218452, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 14317);