Finite Group DatabasebetaFinite Group Databasebeta| order | 10144 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C317 ⋊ C4⋊C8 |
38 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,317|a^2=d,b^2=c,d^2=e,b^a=bc,f^b=f^3162548 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4⋊C8×D317, C2×#23778709, #35203245, … |
| maximal normal subgroup of | C4⋊C8×D317, C2×#23778709, #35203245, … |
| maximal quotient of | #35202973, #35202975, #35202977, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10144, 75);