Finite Group DatabasebetaFinite Group Databasebeta| order | 10016 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×D4×D313 |
| Fitting | C2×D4×C313 ⋊ C2 |
| Sylow | C313 ⋊ C22×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D313 |
| commutator, cosocle | C2×C313 | C24 |
| Frattini | C2 | C23×D313 |
| Fitting | C2×D4×C313 | C2 |
| socle | C22×C313 | C23 |
| hypercenter | C2×D4 | D313 |
| hypocenter | C313 | C22×D4 |
| LCS | G ▷ C2×C313 ▷ C313 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
236 conjugacy classes of subgroups.
1580 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #99×D313, #100×D313, #102×D313, … |
| maximal normal subgroup of | #99×D313, #100×D313, #102×D313, … |
| maximal quotient of | C2×C22⋊C4×D313, C2×C4⋊C4×D313, C4×D4×D313, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10016, 182);