Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #108×C277 ⋊ C2 |
| Sylow | C277 ⋊ #430 |
102 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4432 |
Polycyclic presentation:
2^6,277|a^2=e,b^2=d,d^2=f,e^2=f,b^a=bd,d^a=df,c^b=cf,g^c=g^2761954 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #47985380, #47985383, #47985385, … |
| maximal normal subgroup of | #47985380, #47985383, #47985385, … |
| maximal quotient of | #47981916, #47981918, #47981931, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 596);