Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| isoclinism | isoclinic class of Q8⋊(C13⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C22×Q8⋊(C13⋊C3) |
| Fitting, Hall | C22×Q8×C13 ⋊ C3 |
| derived | Q8×C13 ⋊ C22×C3 |
| Sylow | C22×Q8 ⋊ C13⋊C3 |
| Sylow | C13 ⋊ C22×SL(2,𝔽3) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | C22⋊(C13⋊C3) |
| commutator, cosocle, hypocenter | Q8×C13 | C22×C3 |
| Frattini | C2 | C22×C22⋊(C13⋊C3) |
| Fitting | C22×Q8×C13 | C3 |
| socle | C23×C13 | A4 |
| LCS | G ▷ Q8×C13 | |
| UCS | C1 ◁ C23 | |
122 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
108 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 1374);