Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C277 ⋊ #364 |
46 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4432 |
Polycyclic presentation:
2^6,277|a^2=d,b^2=c,c^2=f,d^2=e,e^2=f,b^a=bc,c^a=cf,g^b=g^2762788 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #364×D277, C2×#31799822, #47984931, … |
| maximal normal subgroup of | #364×D277, C2×#31799822, #47984931, … |
| maximal quotient of | #47981230, #47981236, #47981248, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 369);