Finite Group DatabasebetaFinite Group Databasebeta| order | 1184 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | Q8×C37 ⋊ C4 |
| Sylow | C37 ⋊ #103 |
42 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 296 |
Polycyclic presentation:
2^5,37|a^2=d,b^2=e,c^2=e,b^a=bc,c^a=ce,f^a=f^31,c^b=ce,f^d=f^3659 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#11924599, #14558523, #14558524, … |
| maximal normal subgroup of | C2×#11924599, #14558523, #14558524, … |
| maximal quotient of | Q8⋊#64438, #14558383, #14558386, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1184, 209);