Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C127 ⋊ #427 |
114 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,127|a^2=e,b^2=d,c^2=f,d^2=f,b^a=bd,d^a=df,g^b=g^1261288 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30638608, #30638610, #30638613, … |
| maximal normal subgroup of | #30638608, #30638610, #30638613, … |
| maximal quotient of | #30637476, #30637491, #30637508, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 585);