Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #95×C277 ⋊ C2 |
| Sylow | C277 ⋊ #380 |
234 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 8864 |
Polycyclic presentation:
2^6,277|a^2=f,b^2=d,b^a=bd,c^a=ce,g^b=g^276,g^c=g^2762788 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #47981707, #47981709, #47981733, … |
| maximal normal subgroup of | #47981707, #47981709, #47981733, … |
| maximal quotient of | #47981388, #47981392, #47981395, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 408);