Finite Group DatabasebetaFinite Group Databasebeta| order | 10144 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C22⋊C4×C317 ⋊ C2 |
| Sylow | C317 ⋊ #124 |
76 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,317|b^2=e,c^2=d,b^a=bd,c^a=ce,f^c=f^3161594 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #124×D317, C2×#23778766, #35203750, … |
| maximal normal subgroup of | #124×D317, C2×#23778766, #35203750, … |
| maximal quotient of | #35203087, #35203111, #35203112, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10144, 132);