Finite Group DatabasebetaFinite Group Databasebeta| order | 1872 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C3×D13⋊SL(2,𝔽3) |
| unambiguous semidirect product | (C3×D13)⋊SL(2,𝔽3) |
| Fitting | C3×Q8×C13 ⋊ C2×C3 |
| derived | Q8×C13 ⋊ C2×C32 |
| Hall | Q8×D13 ⋊ C32 |
| Sylow | C13 ⋊ C2×C3×SL(2,𝔽3) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D13⋊A4 |
| commutator, cosocle, hypocenter | Q8×C13 | C2×C32 |
| Frattini | C2 | C3×D13⋊A4 |
| Fitting | C3×Q8×C13 | C2×C3 |
| socle | C2×C3×C13 | C2×A4 |
| LCS | G ▷ Q8×C13 | |
| UCS | C1 ◁ C2×C3 | |
100 conjugacy classes of subgroups.
| transitive degree | μt(G) = 312 |
72 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1872, 768);