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,c^b=cf,g^b=g^1662696 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36322223, #36322225, #36322226, … |
| maximal normal subgroup of | #36322223, #36322225, #36322226, … |
| maximal quotient of | C8×#14581934, #36322421, #36322427, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 504);