Finite Group DatabasebetaFinite Group Databasebeta| order | 10144 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | SD16×C317 ⋊ C2 |
| Sylow | C317 ⋊ #137 |
60 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,317|b^2=e,d^2=e,b^a=bd,c^a=ce,d^a=de,d^b=de,f^c=f^3161117 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #137×D317, C2×#23778809, #35204019, … |
| maximal normal subgroup of | #137×D317, C2×#23778809, #35204019, … |
| maximal quotient of | #35203221, #35203230, #35203262, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10144, 175);