Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×SL(2,𝔽3)×D13 |
| Fitting | C2×Q8×C13 ⋊ C2×C3 |
| derived | Q8×C13 ⋊ C22×C3 |
| Hall | C2×Q8×D13 ⋊ C3 |
| Sylow | C13 ⋊ C22×SL(2,𝔽3) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | A4×D13 |
| commutator, cosocle, hypocenter | Q8×C13 | C22×C3 |
| Frattini | C2 | C2×A4×D13 |
| Fitting | C2×Q8×C13 | C2×C3 |
| socle | C22×C13 | C2×A4 |
| LCS | G ▷ Q8×C13 | |
| UCS | C1 ◁ C22 | |
122 conjugacy classes of subgroups.
| transitive degree | μt(G) = 208 |
112 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 1261);