Finite Group DatabasebetaFinite Group Databasebeta| order | 15939 |
| isoclinism | isoclinic class of C23⋊C11 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C7×C11 · Schur multiplier (H2) = C3 |
| Fitting, socle, Hall | C32×C7×C23 ⋊ C11 |
| derived, Sylow | C23 ⋊ C32×C7×C11 |
| Hall | C32×C23 ⋊ C7×C11 |
| Hall | C7×C23 ⋊ C32×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C7 | C23⋊C11 |
| commutator, cosocle, hypocenter | C23 | C32×C7×C11 |
| Frattini | C1 | G |
| Fitting, socle | C32×C7×C23 | C11 |
| LCS | G ▷ C23 | |
| UCS | C1 ◁ C32×C7 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1449 |
819 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×C7×AGL(1,𝔽23), C32×C7⋊AGL(1,𝔽23), C32×D7×C23⋊C11, … |
| maximal normal subgroup of | C32×C7×AGL(1,𝔽23), C32×C7⋊AGL(1,𝔽23), C32×D7×C23⋊C11, … |
| maximal quotient of | C2×C32×C7×C23⋊C11 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15939, 7);