Finite Group DatabasebetaFinite Group Databasebeta| order | 13915 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×C121⋊C5 |
| unambiguous semidirect product | C121⋊(C5×C23) |
| unambiguous semidirect product | (C23×C121)⋊C5 |
| Fitting, Hall | C23×C121 ⋊ C5 |
| derived, Sylow | C121 ⋊ C5×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | C121⋊C5 |
| commutator, cosocle, hypocenter | C121 | C5×C23 |
| Frattini | C11 | C23×C11⋊C5 |
| Fitting | C23×C121 | C5 |
| socle | C11×C23 | C11⋊C5 |
| LCS | G ▷ C121 | |
| UCS | C1 ◁ C23 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2783 |
667 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C23×C121⋊C5, D23×C121⋊C5, C23×D121⋊C5, … |
| maximal normal subgroup of | C2×C23×C121⋊C5, D23×C121⋊C5, C23×D121⋊C5, … |
| maximal quotient of | C2×C23×C121⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13915, 3);