Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C277 ⋊ #442 |
132 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8864 |
Polycyclic presentation:
2^6,277|a^2=e,c^2=ef,d^2=f,b^a=bd,c^a=cf,d^a=df,g^a=g^276,d^b=df,g^c=g^2761954 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #47985066, #47985068 |
| maximal normal subgroup of | #47985066, #47985068 |
| maximal quotient of | #47981991, #47982032, #47982081, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 661);