Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C22×Q8×C277 ⋊ C2 |
| Sylow | C277 ⋊ #448 |
158 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8864 |
Polycyclic presentation:
2^6,277|b^2=f,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^276,d^b=df2779 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #47982117, #47982118, #47982128, … |
| maximal normal subgroup of | #47982117, #47982118, #47982128, … |
| maximal quotient of | #47982090, #47982107, #47982158, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 688);