Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C277 ⋊ #322 |
66 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17728 |
Polycyclic presentation:
2^6,277|a^2=c,b^2=d,c^2=e,d^2=f,b^a=be,g^b=g^2764456 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #47981087, #47981089, #47981142, … |
| maximal normal subgroup of | #47981087, #47981089, #47981142, … |
| maximal quotient of | #47980994, #47981085, #47981087, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 270);