Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#15689176 |
| Sylow | C47 ⋊ C2×#431 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C42 | C2×D47 |
| commutator | C2×C47 | C23×C8 |
| Frattini | C2×C4 | C23×D47 |
| Fitting | C22×C42×C47 | C2 |
| socle | C23×C47 | C22×C4 |
| hypercenter | C22×C42 | D47 |
| hypocenter | C47 | C2×#431 |
| LCS | G ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C2×C42 ◁ C22×C42 | |
528 conjugacy classes of subgroups.
1552 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #26105659, #26105660, #26105663, … |
| maximal normal subgroup of | #26105659, #26105660, #26105663, … |
| maximal quotient of | C2×#20243134, C2×C4×C22⋊(C47⋊C8), C2×C4×C4⋊(C47⋊C8), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 13126);