Finite Group DatabasebetaFinite Group Databasebeta| order | 16590 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊((C79⋊C3)⋊D7) |
| unambiguous semidirect product | (C79⋊C3)⋊D35 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C7×C79 | C2×C3 |
| LCS | G ▷ C5×C7×C79 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2765 |
Polycyclic presentation:
2,3,5,7,79|c^a=c^4,d^a=d^6,e^a=e^78,e^b=e^23512 conjugacy classes — view the full character table.
| maximal subgroup of | D35×D79⋊C3, D7×C5⋊(D79⋊C3), D5×(C79⋊C3)⋊D7, … |
| maximal normal subgroup of | D35×D79⋊C3, D7×C5⋊(D79⋊C3), D5×(C79⋊C3)⋊D7, … |
| maximal quotient of | (C79⋊C3)⋊Dic35, C2×C5⋊((C79⋊C3)⋊D7) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16590, 45);