Finite Group DatabasebetaFinite Group Databasebeta| order | 10144 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | M16×C317 ⋊ C2 |
| Sylow | C317 ⋊ #100 |
46 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,317|a^2=d,d^2=e,b^a=bc,c^a=ce,d^b=de,f^b=f^3161591 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #100×D317, C2×#23778696, #35203205, … |
| maximal normal subgroup of | #100×D317, C2×#23778696, #35203205, … |
| maximal quotient of | #35202946, #35202962, #35202966, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10144, 62);