Finite Group DatabasebetaFinite Group Databasebeta| order | 18486 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C13 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C9⋊(D79⋊C13) |
| unambiguous semidirect product | (C79⋊C13)⋊D9 |
| unambiguous semidirect product | D711⋊C13 |
| Fitting, derived, Hall | C9×C79 ⋊ C2×C13 |
| Hall | C9×C79⋊C13 ⋊ C2 |
| Hall | D711 ⋊ C13 |
| Hall | C79⋊C13 ⋊ D9 |
| Sylow | C79 ⋊ C13×D9 |
| Sylow | C9 ⋊ D79⋊C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C9×C79 | C2×C13 |
| Frattini | C3 | C3⋊(D79⋊C13) |
| socle | C3×C79 | D3×C13 |
| LCS | G ▷ C9×C79 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 711 |
Polycyclic presentation:
2,3,13,79,3|b^3=e^2,b^a=b^2e,d^a=d^78,e^a=e^2,d^c=d^18105 conjugacy classes — view the full character table.
| maximal subgroup of | D9×D79⋊C13, C2×C9⋊(D79⋊C13) |
| maximal normal subgroup of | D9×D79⋊C13, C2×C9⋊(D79⋊C13) |
| maximal quotient of | C9⋊(Dic79⋊C13), C2×C9⋊(D79⋊C13) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18486, 17);