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×(C22⋊D13)⋊C3 |
| Fitting | C24×C13 ⋊ C2×C3 |
| Hall | C22×C22⋊D13 ⋊ C3 |
| Hall | C13⋊C3 ⋊ C22×D4 |
| Sylow | C13 ⋊ C22×C3×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C2×D13⋊C3 |
| commutator, cosocle | C2×C13 | C24×C3 |
| Frattini | C2 | C23×D13⋊C3 |
| Fitting | C24×C13 | C2×C3 |
| socle | C23×C13 | C22×C3 |
| hypercenter | C24 | D13⋊C3 |
| hypocenter | C13 | C22×C3×D4 |
| LCS | G ▷ C2×C13 ▷ C13 | |
| UCS | C1 ◁ C23 ◁ C24 | |
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×#88251⋊C3 |
| maximal normal subgroup of | C22×D4×D13⋊C3, C2×#88251⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 1256);