Finite Group DatabasebetaFinite Group Databasebeta| order | 10144 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C22⋊C4×C317 ⋊ C2 |
| Sylow | C317 ⋊ C4×D4 |
94 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,317|a^2=e,c^2=e,b^a=bd,f^c=f^3161600 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×D4×D317, C2×#23778740, C4×#19099573, … |
| maximal normal subgroup of | C4×D4×D317, C2×#23778740, C4×#19099573, … |
| maximal quotient of | #35203070, C22⋊C4×Dic317, #35203074, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10144, 106);