Finite Group DatabasebetaFinite Group Databasebeta| order | 1312 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×C4⋊#4223 |
| unambiguous semidirect product | D41⋊(C4⋊C4) |
| Fitting | C2×C4×C41 ⋊ C4 |
| Sylow | C41 ⋊ C2×C4⋊C4 |
92 conjugacy classes of subgroups.
| transitive degree | μt(G) = 328 |
100 conjugacy classes — view the full character table.
| maximal subgroup of | #14581209, #14581210, #14581215, … |
| maximal normal subgroup of | #14581209, #14581210, #14581215, … |
| maximal quotient of | C2×(C2×#4223)⋊C4, C4×C4⋊#4223, #14581278, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1312, 224);