Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C4⋊C4×C277 ⋊ C2 |
| Sylow | C277 ⋊ #481 |
114 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8864 |
Polycyclic presentation:
2^6,277|c^2=df,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^a=g^276,e^c=ef2779 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #47982185, #47982186, #47982196, … |
| maximal normal subgroup of | #47982185, #47982186, #47982196, … |
| maximal quotient of | #47983257, #47983360, #47983484, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 867);