Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C167 ⋊ #324 |
78 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,167|a^2=d,b^2=e,d^2=f,b^a=bc,c^a=ce,d^b=de,g^b=g^1661682 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #324×D167, C2×#24922994, #36322449, … |
| maximal normal subgroup of | #324×D167, C2×#24922994, #36322449, … |
| maximal quotient of | #36321960, #36321962, #36321980, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 274);