Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C47 ⋊ #2731 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D47 |
| commutator, socle | C23×C47 | C24 |
| Fitting | C2×#124×C47 | C2 |
| hypercenter | C2×#124 | D47 |
| hypocenter | C47 | #2731 |
| LCS | G ▷ C23×C47 ▷ C47 | |
| UCS | C1 ◁ C23 ◁ C2×#124 | |
492 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 492 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|a^2=ef,b^2=e,c^2=e,d^2=ef,b^a=be,c^a=cf,d^a=def,c^b=cg,d^b=de,h^b=h^46676 conjugacy classes — view the full character table.
| maximal subgroup of | #26135313, #26135315, #26135744, … |
| maximal normal subgroup of | #26135313, #26135315, #26135744, … |
| maximal quotient of | #26144093, #26144352, #26144662, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 11518);