Finite Group DatabasebetaFinite Group Databasebeta| order | 10144 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C22⋊C4×C317 ⋊ C2 |
| Sylow | C317 ⋊ #99 |
52 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,317|a^2=d,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 | #99×D317, C2×#23778694, #35203195, … |
| maximal normal subgroup of | #99×D317, C2×#23778694, #35203195, … |
| maximal quotient of | #35202946, #35202948, #35202956, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10144, 60);