Finite Group DatabasebetaFinite Group Databasebeta| order | 18736 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C8×C1171 ⋊ C2 |
| Sylow | C1171 ⋊ SD16 |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9368 |
Polycyclic presentation:
2^4,1171|a^2=d,c^2=d,b^a=bc,c^a=cd,e^a=e^1170,c^b=cd,e^b=e^11704687 conjugacy classes. The character table is too large to display.
| maximal subgroup of | SD16×D1171, C2×#34035519, #49154079, … |
| maximal normal subgroup of | SD16×D1171, C2×#34035519, #49154079, … |
| maximal quotient of | #49153980, #49153983, #49153990, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18736, 29);