Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C47 ⋊ #2586 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D47 |
| commutator, socle | C23×C47 | C24 |
| Fitting | C4×C4⋊C4×C47 | C2 |
| hypercenter | C4×C4⋊C4 | D47 |
| hypocenter | C47 | #2586 |
| LCS | G ▷ C23×C47 ▷ C47 | |
| UCS | C1 ◁ C23 ◁ C4×C4⋊C4 | |
412 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,47|a^2=e,b^2=eg,c^2=eg,d^2=f,b^a=be,c^a=cf,d^a=de,c^b=cg,h^c=h^46958 conjugacy classes — view the full character table.
| maximal subgroup of | D47×#2586, C2×#20248794, #26386624, … |
| maximal normal subgroup of | D47×#2586, C2×#20248794, #26386624, … |
| maximal quotient of | #26138729, #26138735, #26140138, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 9916);