Finite Group DatabasebetaFinite Group Databasebeta| order | 14950 |
| isoclinism | isoclinic class of D115 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C13 · Schur multiplier (H2) = C1 |
| direct product | C5×C13×D115 |
| unambiguous semidirect product | C5⋊(C5×C13×D23) |
| unambiguous semidirect product | C23⋊(C5×D5×C13) |
| Fitting, socle, Hall | C52×C13×C23 ⋊ C2 |
| derived | C5×C23 ⋊ C2×C5×C13 |
| Hall | C52×C23 ⋊ C2×C13 |
| Hall | C52×C13 ⋊ D23 |
| Hall | C13×C23 ⋊ C5×D5 |
| Sylow | C52 ⋊ C13×D23 |
| Sylow | C23 ⋊ C5×D5×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C13 | D115 |
| commutator, cosocle, hypocenter | C5×C23 | C2×C5×C13 |
| Frattini | C1 | G |
| Fitting, socle | C52×C13×C23 | C2 |
| LCS | G ▷ C5×C23 | |
| UCS | C1 ◁ C5×C13 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2990 |
3835 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D5×C13×D23, C5×D13×D115, C5×D65⋊D23, … |
| maximal normal subgroup of | C5×D5×C13×D23, C5×D13×D115, C5×D65⋊D23, … |
| maximal quotient of | C5×C13×Dic115, C2×C5×C13×D115 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14950, 16);