Finite Group DatabasebetaFinite Group Databasebeta| order | 10016 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| direct product | C2×#19097573 |
| derived, Sylow | C313 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #14578818 |
| commutator, hypocenter | C313 | C2×C16 |
| Frattini | C2 | C2×#14578818 |
| Fitting, socle, prime radical | C22×C313 | C8 |
| cosocle | #14578816 | C22 |
| LCS | G ▷ C313 | |
| UCS | C1 ◁ C22 | |
28 conjugacy classes of subgroups.
188 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#19097573, #34095246, C22⋊#19097573, … |
| maximal normal subgroup of | C4×#19097573, #34095246, C22⋊#19097573, … |
| maximal quotient of | C4×#19097573, C22⋊#19097573, C4⋊#19097573, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10016, 240);