Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| isoclinism | isoclinic class of (C13⋊C3)⋊Q8 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C26 |
| direct product | C22×C4⋊(D13⋊C3) |
| Fitting | C22×C4×C13 ⋊ C2×C3 |
| Hall | C22×D52 ⋊ C3 |
| Hall | C13⋊C3 ⋊ C22×D4 |
| Sylow | C13 ⋊ C22×C3×D4 |
472 conjugacy classes of subgroups.
| transitive degree | μt(G) = 208 |
92 conjugacy classes — view the full character table.
| maximal subgroup of | C22×D4×D13⋊C3, C2×#11929141 |
| maximal normal subgroup of | C22×D4×D13⋊C3, C2×#11929141 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 1244);