Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C16×C277 ⋊ C2 |
| Sylow | C277 ⋊ #504 |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8864 |
Polycyclic presentation:
2^6,277|a^2=d,d^2=e,e^2=f,c^b=cf,g^c=g^2764456 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #47981308, #47981310, #47985002, … |
| maximal normal subgroup of | #47981308, #47981310, #47985002, … |
| maximal quotient of | #47984762, #47984763, #47984779, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 965);