Finite Group DatabasebetaFinite Group Databasebeta| order | 888 |
| isoclinism | isoclinic class of A4×D37 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C2 |
| direct product | A4×D37 |
| Fitting, socle, derived | C22×C37 ⋊ C2×C3 |
| Hall | C22×D37 ⋊ C3 |
| Sylow | C37 ⋊ C2×A4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C22×C37 | C2×C3 |
| LCS | G ▷ C22×C37 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 148 |
80 conjugacy classes — view the full character table.
| maximal subgroup of | A4⋊#3866, A4×#3866, S4×D37, … |
| maximal normal subgroup of | A4⋊#3866, A4×#3866, S4×D37, … |
| maximal quotient of | #13183939, SL(2,𝔽3)×D37, A4×Dic37, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(888, 50);