Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C22×C42 |
No aliases for this group.
| Sylow | C47 ⋊ #2379 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D47 |
| commutator | C22×C47 | C23×C4 |
| Fitting | C2×#124×C47 | C2 |
| socle | C23×C47 | C24 |
| hypercenter | C2×#124 | D47 |
| hypocenter | C47 | #2379 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C23 ◁ C2×#124 | |
520 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 213 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,c^2=f,d^2=e,b^a=be,c^a=cf,d^a=def,h^a=h^46,c^b=cef,d^b=de682 conjugacy classes — view the full character table.
| maximal subgroup of | #26110632, #26110635, #26110637, … |
| maximal normal subgroup of | #26110632, #26110635, #26110637, … |
| maximal quotient of | #26137902, #26137913, #26137920, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 7684);