Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C277 ⋊ #533 |
222 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8864 |
Polycyclic presentation:
2^6,277|a^2=f,c^2=f,d^2=e,b^a=be,c^a=cf,g^c=g^2762788 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #47984109, #47984142, #47984146, … |
| maximal normal subgroup of | #47984109, #47984142, #47984146, … |
| maximal quotient of | #47985570, #47985639, #47985649, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 1102);