Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×M16×C157 ⋊ C2 |
| Sylow | C157 ⋊ #436 |
122 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 53 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=e,c^2=e,e^2=f,b^a=bd,c^a=cf,c^b=cf,g^b=g^1561588 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #436×D157, C2×#23757349, #34108836, … |
| maximal normal subgroup of | #436×D157, C2×#23757349, #34108836, … |
| maximal quotient of | #34099019, #34099024, #34099026, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 625);