Finite Group DatabasebetaFinite Group Databasebeta| order | 1184 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×C22⋊#3866 |
| unambiguous semidirect product | D37⋊(C22⋊C4) |
| unambiguous semidirect product | (C2×#3866)⋊C22 |
| Fitting | C23×C37 ⋊ C4 |
| Sylow | C37 ⋊ C2×C22⋊C4 |
132 conjugacy classes of subgroups.
| transitive degree | μt(G) = 296 |
92 conjugacy classes — view the full character table.
| maximal subgroup of | #14558410, #14558411, C4×C22⋊#3866, … |
| maximal normal subgroup of | #14558410, #14558411, C4×C22⋊#3866, … |
| maximal quotient of | C2×(C2×#3866)⋊C4, C4×C22⋊#3866, #14558474, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1184, 223);