Finite Group DatabasebetaFinite Group Databasebeta| order | 912 |
| isoclinism | isoclinic class of A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C19 · Schur multiplier (H2) = C22 |
| direct product | C22×A4×C19 |
| Fitting, socle, Hall | C24×C19 ⋊ C3 |
| derived | C22 ⋊ C22×C3×C19 |
| Sylow | C24 ⋊ C3×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C19 | A4 |
| commutator, cosocle, hypocenter | C22 | C22×C3×C19 |
| Frattini | C1 | G |
| Fitting, socle | C24×C19 | C3 |
| LCS | G ▷ C22 | |
| UCS | C1 ◁ C22×C19 | |
78 conjugacy classes of subgroups.
| transitive degree | μt(G) = 228 |
304 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C19×SL(2,ℤ/4), C19×GL(2,ℤ/4), C2×A4⋊Dic19, … |
| maximal normal subgroup of | C2×C19×SL(2,ℤ/4), C19×GL(2,ℤ/4), C2×A4⋊Dic19, … |
| maximal quotient of | C2×C4×A4×C19, D4×A4×C19, Q8×A4×C19, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(912, 215);