Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C4⋊Q8×C277 ⋊ C2 |
| Sylow | C277 ⋊ #486 |
118 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8864 |
Polycyclic presentation:
2^6,277|b^2=e,c^2=d,d^2=f,e^2=f,b^a=bd,c^a=ce,d^a=df,e^a=ef,g^a=g^276,g^b=g^276,g^c=g^2761954 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #47982256, #47982257, #47982263, … |
| maximal normal subgroup of | #47982256, #47982257, #47982263, … |
| maximal quotient of | #47983294, #47983849, #47983972, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 897);