Finite Group DatabasebetaFinite Group Databasebeta| order | 888 |
| isoclinism | isoclinic class of SL(2,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C37 · Schur multiplier (H2) = C1 |
| direct product | SL(2,𝔽3)×C37 |
| unambiguous semidirect product | Q8⋊(C3×C37) |
| Fitting, Hall | Q8×C37 ⋊ C3 |
| derived, Sylow | Q8 ⋊ C3×C37 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C2×C37 | A4 |
| commutator, cosocle, hypocenter | Q8 | C3×C37 |
| Frattini | C2 | A4×C37 |
| Fitting | Q8×C37 | C3 |
| LCS | G ▷ Q8 | |
| UCS | C1 ◁ C2×C37 | |
14 conjugacy classes of subgroups.
| transitive degree | μt(G) = 296 |
259 conjugacy classes. The character table is too large to display.
| derived subgroup of | C37⋊#226, C37⋊GL(2,𝔽3) |
| maximal subgroup of | C37×#226, C37×GL(2,𝔽3), C37⋊#226, … |
| maximal normal subgroup of | C37×#226, C37×GL(2,𝔽3), C37⋊#226, … |
| maximal quotient of | C2×SL(2,𝔽3)×C37 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(888, 25);