Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C8 |
No aliases for this group.
| Sylow | C47 ⋊ #1450 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C8 | C2×D47 |
| commutator | C2×C47 | C2×C4×C8 |
| Frattini | C42 | C22×D47 |
| Fitting | C2×C4×C8×C47 | C2 |
| socle | C22×C47 | C2×C42 |
| hypercenter | C2×C4×C8 | D47 |
| hypocenter | C47 | #1450 |
| LCS | G ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C4×C8 ◁ C2×C4×C8 | |
212 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,47|a^2=d,b^2=e,d^2=f,e^2=g,c^b=cf,h^b=h^461552 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #26103113, #26103115, #26103116, … |
| maximal normal subgroup of | #26103113, #26103115, #26103116, … |
| maximal quotient of | #26105634, #26105663, #26106707, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 2793);