Finite Group DatabasebetaFinite Group Databasebeta| order | 10144 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C4⋊C4×C317 ⋊ C2 |
| Sylow | C317 ⋊ #117 |
76 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,317|a^2=e,c^2=d,b^a=bd,f^b=f^316,f^c=f^3161600 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35203216, #35203218, #35203226, … |
| maximal normal subgroup of | #35203216, #35203218, #35203226, … |
| maximal quotient of | #35203068, #35203070, C4⋊C4×Dic317, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10144, 104);