Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C167 ⋊ #364 |
46 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,167|a^2=d,b^2=c,c^2=f,d^2=e,e^2=f,b^a=bc,c^a=cf,g^b=g^1661688 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #364×D167, C2×#24923089, #36325902, … |
| maximal normal subgroup of | #364×D167, C2×#24923089, #36325902, … |
| maximal quotient of | #36322201, #36322207, #36322219, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 369);