Finite Group DatabasebetaFinite Group Databasebeta| order | 1184 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×D4×C37 ⋊ C2 |
| Sylow | C37 ⋊ AGL(1,ℤ/8) |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 296 |
Polycyclic presentation:
2^5,37|d^2=e,b^a=bd,c^a=ce,d^a=de,f^a=f^36,d^b=de191 conjugacy classes — view the full character table.
| maximal subgroup of | #14557699, #14557700, #14557704, … |
| maximal normal subgroup of | #14557699, #14557700, #14557704, … |
| maximal quotient of | #14557532, #14557538, #14557573, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1184, 172);