Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C4⋊C4×C157 ⋊ C4 |
| Sylow | C157 ⋊ #387 |
154 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,157|a^2=f,b^2=f,c^2=d,b^a=bd,c^a=ce,g^a=g^28,g^b=g^129,g^f=g^156418 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#23758222, #34116590, #34116595, … |
| maximal normal subgroup of | C2×#23758222, #34116590, #34116595, … |
| maximal quotient of | #34115311, #34115315, #34115316, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 1498);