Finite Group DatabasebetaFinite Group Databasebeta| order | 10144 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C22⋊C4×C317 ⋊ C2 |
| Sylow | C317 ⋊ #123 |
78 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,317|c^2=d,b^a=bd,c^a=ce,f^a=f^316,f^c=f^3161594 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35203414, #123×D317, C2×#23778764, … |
| maximal normal subgroup of | #35203414, #123×D317, C2×#23778764, … |
| maximal quotient of | #35203084, #35203098, #35203100, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10144, 130);