Finite Group DatabasebetaFinite Group Databasebeta| order | 888 |
| isoclinism | isoclinic class of C22⋊(C37⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×C22⋊(C37⋊C3) |
| unambiguous semidirect product | C23⋊(C37⋊C3) |
| unambiguous semidirect product | (C2×C37)⋊A4 |
| Fitting, socle, Hall | C23×C37 ⋊ C3 |
| derived | C22×C37 ⋊ C2×C3 |
| Sylow | C37 ⋊ C2×A4 |
| Sylow | C23 ⋊ C37⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C22⋊(C37⋊C3) |
| commutator, cosocle, hypocenter | C22×C37 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C23×C37 | C3 |
| LCS | G ▷ C22×C37 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 222 |
104 conjugacy classes — view the full character table.
| maximal subgroup of | Dic37⋊A4, C4×C22⋊(C37⋊C3), C2×D37⋊A4, … |
| maximal normal subgroup of | Dic37⋊A4, C4×C22⋊(C37⋊C3), C2×D37⋊A4, … |
| maximal quotient of | C4×C22⋊(C37⋊C3), C2×Q8⋊(C37⋊C3), #41⋊(C37⋊C3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(888, 57);