Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×#125×C47 ⋊ C2 |
| Sylow | C47 ⋊ #2556 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D47 |
| commutator, socle | C23×C47 | C24 |
| Fitting | C2×#125×C47 | C2 |
| hypercenter | C2×#125 | D47 |
| hypocenter | C47 | #2556 |
| LCS | G ▷ C23×C47 ▷ C47 | |
| UCS | C1 ◁ C23 ◁ C2×#125 | |
492 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,47|a^2=e,b^2=eg,c^2=e,d^2=f,b^a=be,c^a=cf,d^a=de,c^b=cg,h^b=h^46682 conjugacy classes — view the full character table.
| maximal subgroup of | D47×#2556, C2×#20248468, #26386461, … |
| maximal normal subgroup of | D47×#2556, C2×#20248468, #26386461, … |
| maximal quotient of | #26138600, #26138734, #26139548, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 9590);