Finite Group DatabasebetaFinite Group Databasebeta| order | 14272 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×C22⋊C4×C223 ⋊ C2 |
| Sylow | C223 ⋊ #379 |
506 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 506 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 3568 |
Polycyclic presentation:
2^6,223|a^2=f,b^a=bd,c^a=ce,g^c=g^2222248 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #43252720 |
| maximal normal subgroup of | #43252720 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14272, 404);