Finite Group DatabasebetaFinite Group Databasebeta| order | 14950 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C5⋊D1495 |
| unambiguous semidirect product | C13⋊(C5⋊D115) |
| unambiguous semidirect product | C23⋊(C5⋊D65) |
| Fitting, socle, derived, Hall | C52×C13×C23 ⋊ C2 |
| Hall | C52×C23 ⋊ D13 |
| Hall | C52×C13 ⋊ D23 |
| Hall | C13×C23 ⋊ C5⋊D5 |
| Sylow | C52 ⋊ D299 |
| Sylow | C23 ⋊ C5⋊D65 |
| Sylow | C13 ⋊ C5⋊D115 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C13×C23 | C2 |
| LCS | G ▷ C52×C13×C23 | |
| UCS | C1 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7475 |
Polycyclic presentation:
2,5^2,13,23|b^a=b^4,c^a=c^4,d^a=d^12,e^a=e^223739 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D5×D1495, D65×D115, D23×C5⋊D65, … |
| maximal normal subgroup of | D5×D1495, D65×D115, D23×C5⋊D65, … |
| maximal quotient of | C23⋊#13049918, C2×C5⋊D1495 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14950, 10);