Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Sylow | C47 ⋊ #2280 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D47 |
| commutator | C22×C47 | C23×C4 |
| Frattini | C23 | C23×D47 |
| Fitting | C24×C4×C47 | C2 |
| socle | C23×C47 | C24 |
| hypercenter | C24×C4 | D47 |
| hypocenter | C47 | #2280 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C22×C4 ◁ C24×C4 | |
1088 conjugacy classes of subgroups; only the 341 normal subgroups are shown.
This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 341 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=g,d^2=e,b^a=be,c^a=cf,h^a=h^461528 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #26105933, #26105934, #26105941, … |
| maximal normal subgroup of | #26105933, #26105934, #26105941, … |
| maximal quotient of | #26137379, #26137394, C4×#15688979, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 6893);