Finite Group DatabasebetaFinite Group Databasebeta| order | 13915 |
| isoclinism | isoclinic class of C23⋊C11 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C112 · Schur multiplier (H2) = C11 |
| direct product | C5×C11×C23⋊C11 |
| unambiguous semidirect product | C23⋊(C5×C112) |
| unambiguous semidirect product | (C5×C23)⋊C112 |
| unambiguous semidirect product | (C5×C11×C23)⋊C11 |
| Fitting, socle | C5×C11×C23 ⋊ C11 |
| derived, Sylow | C23 ⋊ C5×C112 |
| Hall | C5×C23 ⋊ C112 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C11 | C23⋊C11 |
| commutator, cosocle, hypocenter | C23 | C5×C112 |
| Frattini | C1 | G |
| Fitting, socle | C5×C11×C23 | C11 |
| LCS | G ▷ C23 | |
| UCS | C1 ◁ C5×C11 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1265 |
715 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×C11×AGL(1,𝔽23), C5×C11⋊AGL(1,𝔽23), C5×D11×C23⋊C11, … |
| maximal normal subgroup of | C5×C11×AGL(1,𝔽23), C5×C11⋊AGL(1,𝔽23), C5×D11×C23⋊C11, … |
| maximal quotient of | C2×C5×C11×C23⋊C11 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13915, 6);