Finite Group DatabasebetaFinite Group Databasebeta| order | 16951 |
| isoclinism | isoclinic class of C23⋊C11 |
| automorphism | ? |
| homology | Abelianization (H1) = C11×C67 · Schur multiplier (H2) = C1 |
| direct product | C67×C23⋊C11 |
| unambiguous semidirect product | C23⋊(C11×C67) |
| Fitting, socle, Hall | C23×C67 ⋊ C11 |
| derived, Sylow | C23 ⋊ C11×C67 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C67 | C23⋊C11 |
| commutator, cosocle, hypocenter | C23 | C11×C67 |
| Frattini | C1 | G |
| Fitting, socle | C23×C67 | C11 |
| LCS | G ▷ C23 | |
| UCS | C1 ◁ C67 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1541 |
871 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C67×C23⋊C11, D67×C23⋊C11, C67×AGL(1,𝔽23), … |
| maximal normal subgroup of | C2×C67×C23⋊C11, D67×C23⋊C11, C67×AGL(1,𝔽23), … |
| maximal quotient of | C2×C67×C23⋊C11 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16951, 1);