Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C4⋊C4×C167 ⋊ C2 |
| Sylow | C167 ⋊ #554 |
228 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,167|a^2=e,b^2=ef,d^2=e,b^a=be,c^a=cf,d^b=de,g^c=g^1661685 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36335958, #36335960, #36336010, … |
| maximal normal subgroup of | #36335958, #36335960, #36336010, … |
| maximal quotient of | #36327011, #36327015, C4⋊C4×C22⋊D167, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 1254);