Finite Group DatabasebetaFinite Group Databasebeta| order | 10016 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | M16×D313 |
| Fitting | M16×C313 ⋊ C2 |
| Sylow | C313 ⋊ C2×M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×D313 |
| commutator, socle | C2×C313 | C22×C4 |
| Fitting | M16×C313 | C2 |
| prime radical | C22×D313 | C4 |
| cosocle | C4×C313 | C23 |
| hypercenter | M16 | D313 |
| hypocenter | C313 | C2×M16 |
| LCS | G ▷ C2×C313 ▷ C313 | |
| UCS | C1 ◁ C4 ◁ M16 | |
68 conjugacy classes of subgroups.
1580 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #100×D313, #101×D313, #34094133, … |
| maximal normal subgroup of | #100×D313, #101×D313, #34094133, … |
| maximal quotient of | #97×D313, M16×Dic313, #34094104, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10016, 149);