Finite Group DatabasebetaFinite Group Databasebeta| order | 528 |
| isoclinism | isoclinic class of SL(2,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1 |
| direct product | C2×C11×SL(2,𝔽3) |
| unambiguous semidirect product | (C2×Q8)⋊(C3×C11) |
| unambiguous semidirect product | (C2×Q8×C11)⋊C3 |
| Fitting, Hall | C2×Q8×C11 ⋊ C3 |
| derived | Q8 ⋊ C2×C3×C11 |
| Sylow | C2×Q8 ⋊ C3×C11 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C22×C11 | A4 |
| commutator, cosocle, hypocenter | Q8 | C2×C3×C11 |
| Frattini | C2 | C2×C11×A4 |
| Fitting | C2×Q8×C11 | C3 |
| LCS | G ▷ Q8 | |
| UCS | C1 ◁ C22×C11 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 176 |
154 conjugacy classes — view the full character table.
| maximal subgroup of | C11×#859, C11⋊#859, SL(2,𝔽3)×Dic11, … |
| maximal normal subgroup of | C11×#859, C11⋊#859, SL(2,𝔽3)×Dic11, … |
| maximal quotient of | C4×C11×SL(2,𝔽3), C22×C11×SL(2,𝔽3), C2×C11×Q8⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(528, 124);