Finite Group DatabasebetaFinite Group Databasebeta| order | 10016 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×#19097569 |
| derived, Sylow | C313 ⋊ C22×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | #11929411 |
| commutator, hypocenter | C313 | C22×C8 |
| Frattini | C2 | C22×#11929411 |
| Fitting | C2×C4×C313 | C4 |
| socle | C22×C313 | C2×C4 |
| prime radical | C22×D313 | C4 |
| cosocle | Dic313 | C23 |
| LCS | G ▷ C313 | |
| UCS | C1 ◁ C2×C4 | |
76 conjugacy classes of subgroups.
656 conjugacy classes — view the full character table.
| maximal subgroup of | #34095017, #34095025, #34095027, … |
| maximal normal subgroup of | #34095017, #34095025, #34095027, … |
| maximal quotient of | C2×C4×#14578816, C4×#19097569, #34095120, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10016, 229);