Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C167 ⋊ #405 |
130 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,167|a^2=d,b^2=e,d^2=f,g^a=g^166,c^b=cf,g^b=g^1661700 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36323892, #36323894, #36323937, … |
| maximal normal subgroup of | #36323892, #36323894, #36323937, … |
| maximal quotient of | M16×C167⋊C8, #36322422, #36322425, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 507);