Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | C2×#15689722 |
| Fitting | C2×C22⋊Q8×C47 ⋊ C2 |
| Sylow | C47 ⋊ C2×#539 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D47 |
| commutator | C22×C47 | C25 |
| Frattini | C22 | C24×D47 |
| Fitting | C2×C22⋊Q8×C47 | C2 |
| socle | C23×C47 | C24 |
| hypercenter | C2×C22⋊Q8 | D47 |
| hypocenter | C47 | C2×#539 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C23 ◁ C2×C22⋊Q8 | |
1144 conjugacy classes of subgroups.
688 conjugacy classes — view the full character table.
| maximal subgroup of | #26108100, #26108104, C2×#20242316, … |
| maximal normal subgroup of | #26108100, #26108104, C2×#20242316, … |
| maximal quotient of | C2×#20245990, C2×#20246016, C2×#20246056, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 17863);