Finite Group DatabasebetaFinite Group Databasebeta| order | 888 |
| isoclinism | isoclinic class of A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C37 · Schur multiplier (H2) = C2 |
| direct product | C2×A4×C37 |
| unambiguous semidirect product | C23⋊(C3×C37) |
| Fitting, socle, Hall | C23×C37 ⋊ C3 |
| derived | C22 ⋊ C2×C3×C37 |
| Sylow | C23 ⋊ C3×C37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C37 | A4 |
| commutator, cosocle, hypocenter | C22 | C2×C3×C37 |
| Frattini | C1 | G |
| Fitting, socle | C23×C37 | C3 |
| LCS | G ▷ C22 | |
| UCS | C1 ◁ C2×C37 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 222 |
296 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C37×SL(2,ℤ/4), A4⋊Dic37, A4×Dic37, … |
| maximal normal subgroup of | C37×SL(2,ℤ/4), A4⋊Dic37, A4×Dic37, … |
| maximal quotient of | C4×A4×C37, C2×SL(2,𝔽3)×C37, C37×#41⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(888, 56);