Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #104×C157 ⋊ C2 |
| Sylow | C157 ⋊ #456 |
142 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 39 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,c^2=f,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^156,d^b=df,e^b=ef,d^c=df,g^c=g^1561108 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #456×D157, C2×#23757457, #34109481, … |
| maximal normal subgroup of | #456×D157, C2×#23757457, #34109481, … |
| maximal quotient of | #34099100, #34099102, #34099106, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 733);