Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C47×#398 ⋊ C2 |
| Sylow | C47 ⋊ #2609 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D47 |
| commutator, socle | C23×C47 | C24 |
| Fitting | C47×#398 | C2 |
| hypercenter | #398 | D47 |
| hypocenter | C47 | #2609 |
| LCS | G ▷ C23×C47 ▷ C47 | |
| UCS | C1 ◁ C23 ◁ #398 | |
540 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 137 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,47|b^2=eg,d^2=g,b^a=be,c^a=cf,d^a=de,h^a=h^46,c^b=cg,h^c=h^46,h^d=h^46544 conjugacy classes — view the full character table.
| maximal subgroup of | #26128695, #26128699, #26129281, … |
| maximal normal subgroup of | #26128695, #26128699, #26129281, … |
| maximal quotient of | #26138971, #26140229, #26140252, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 10188);