Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | C2×C13⋊GL(2,𝔽3) |
| unambiguous semidirect product | (C2×C13)⋊GL(2,𝔽3) |
| Fitting | C2×Q8×C13 ⋊ D3 |
| derived | C13×SL(2,𝔽3) ⋊ C22 |
| Sylow | C13 ⋊ C2×GL(2,𝔽3) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | A4⋊D13 |
| commutator, cosocle, hypocenter | C13×SL(2,𝔽3) | C22 |
| Frattini | C2 | C2×A4⋊D13 |
| Fitting | C2×Q8×C13 | D3 |
| socle | C22×C13 | S4 |
| LCS | G ▷ C13×SL(2,𝔽3) | |
| UCS | C1 ◁ C22 | |
102 conjugacy classes of subgroups.
| transitive degree | μt(G) = 208 |
100 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 1235);