Finite Group DatabasebetaFinite Group Databasebeta| order | 12128 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M16×C379 ⋊ C2 |
| Sylow | C379 ⋊ AGL(1,ℤ/8) |
68 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,379|d^2=e,b^a=bd,c^a=ce,d^a=de,f^a=f^378,d^b=de,f^b=f^3781901 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37565413, #37565414, #37565418, … |
| maximal normal subgroup of | #37565413, #37565414, #37565418, … |
| maximal quotient of | #37565246, #37565250, #37565286, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12128, 174);