Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C2×D8×C277 ⋊ C2 |
| Sylow | C277 ⋊ #469 |
130 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8864 |
Polycyclic presentation:
2^6,277|b^2=df,d^2=f,b^a=bd,c^a=ce,d^a=df,c^b=cf,g^c=g^2761948 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #47985111, #47985380 |
| maximal normal subgroup of | #47985111, #47985380 |
| maximal quotient of | #47982643, #47982648, #47982677, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 799);