Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C167 ⋊ #441 |
108 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,167|a^2=e,b^2=f,c^2=e,d^2=f,b^a=bd,c^a=cf,d^a=df,g^a=g^166,d^b=df,g^c=g^1661184 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36326030, #36326032, #441×D167, … |
| maximal normal subgroup of | #36326030, #36326032, #441×D167, … |
| maximal quotient of | #36322957, #36323010, #36323047, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 656);