Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C47 ⋊ #2803 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D47 |
| commutator, socle | C23×C47 | C24 |
| Fitting | C47×#392 | C2 |
| hypercenter | #392 | D47 |
| hypocenter | C47 | #2803 |
| LCS | G ▷ C23×C47 ▷ C47 | |
| UCS | C1 ◁ C23 ◁ #392 | |
470 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,47|a^2=efg,b^2=e,c^2=eg,d^2=ef,b^a=be,c^a=cf,d^a=def,h^a=h^46,c^b=cg,d^b=de,h^b=h^46,h^c=h^46538 conjugacy classes — view the full character table.
| maximal subgroup of | #26424167, #26424175, #26424327, … |
| maximal normal subgroup of | #26424167, #26424175, #26424327, … |
| maximal quotient of | #26144670, #26144734, #26144762, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 12449);