Finite Group DatabasebetaFinite Group Databasebeta| order | 912 |
| isoclinism | isoclinic class of Q8⋊(C19⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C2×Q8⋊(C19⋊C3) |
| unambiguous semidirect product | (C2×Q8)⋊(C19⋊C3) |
| unambiguous semidirect product | (C2×C19)⋊SL(2,𝔽3) |
| Fitting, Hall | C2×Q8×C19 ⋊ C3 |
| derived | Q8×C19 ⋊ C2×C3 |
| Sylow | C19 ⋊ C2×SL(2,𝔽3) |
| Sylow | C2×Q8 ⋊ C19⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | C22⋊(C19⋊C3) |
| commutator, cosocle, hypocenter | Q8×C19 | C2×C3 |
| Frattini | C2 | C2×C22⋊(C19⋊C3) |
| Fitting | C2×Q8×C19 | C3 |
| socle | C22×C19 | A4 |
| LCS | G ▷ Q8×C19 | |
| UCS | C1 ◁ C22 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 304 |
74 conjugacy classes — view the full character table.
| maximal subgroup of | Dic19⋊SL(2,𝔽3), C4×Q8⋊(C19⋊C3), C2×#11744922, … |
| maximal normal subgroup of | Dic19⋊SL(2,𝔽3), C4×Q8⋊(C19⋊C3), C2×#11744922, … |
| maximal quotient of | C4×Q8⋊(C19⋊C3), C22×Q8⋊(C19⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(912, 171);