Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C277 ⋊ #518 |
338 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4432 |
Polycyclic presentation:
2^6,277|a^2=f,b^a=be,d^a=de,g^a=g^276,c^b=ce2794 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #47983273, #47983276, #47983376, … |
| maximal normal subgroup of | #47983273, #47983276, #47983376, … |
| maximal quotient of | #47985520, #47985524, #47985528, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 1024);