Finite Group DatabasebetaFinite Group Databasebeta| order | 10016 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C8×C313 ⋊ C2 |
| Sylow | C313 ⋊ C22⋊C8 |
50 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,313|a^2=d,d^2=e,b^a=bc,f^b=f^3122516 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22⋊C8×D313, C2×#23756409, #34094114, … |
| maximal normal subgroup of | C22⋊C8×D313, C2×#23756409, #34094114, … |
| maximal quotient of | #34093875, #34093877, #34093879, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10016, 58);