Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | #97×C277 ⋊ C2 |
| Sylow | C277 ⋊ C4×M16 |
142 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8864 |
Polycyclic presentation:
2^6,277|a^2=d,b^2=e,d^2=f,c^a=cf,g^b=g^276,g^c=g^2762800 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #47981752, #47981754, #47981757, … |
| maximal normal subgroup of | #47981752, #47981754, #47981757, … |
| maximal quotient of | #47981446, #47981455, #47981463, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 501);