Finite Group DatabasebetaFinite Group Databasebeta| order | 1184 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | D4×C37 ⋊ C4 |
| Sylow | C37 ⋊ #104 |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 296 |
Polycyclic presentation:
2^5,37|a^2=d,c^2=e,d^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×#11924600, D37⋊#104, #14558530, … |
| maximal normal subgroup of | C2×#11924600, D37⋊#104, #14558530, … |
| maximal quotient of | D4⋊#64438, #14558383, #14558384, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1184, 210);