Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C4×C8×C47 ⋊ C2 |
| Sylow | C47 ⋊ #2931 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8 | C22×D47 |
| commutator, socle | C22×C47 | C23×C4 |
| Frattini | C2×C4 | C23×D47 |
| Fitting | C2×C4×C8×C47 | C2 |
| hypercenter | C2×C4×C8 | D47 |
| hypocenter | C47 | #2931 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C2×C8 ◁ C2×C4×C8 | |
500 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 197 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=f,c^2=f,f^2=g,b^a=be,d^a=dg,h^a=h^46,d^b=dg,h^b=h^461528 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #26107282, #26107292, #26107303, … |
| maximal normal subgroup of | #26107282, #26107292, #26107303, … |
| maximal quotient of | #26186795, #26186803, #26186811, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 13223);