Finite Group DatabasebetaFinite Group Databasebeta| order | 16590 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊#15693303 |
| 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,d^b=d^2,e^b=e^55511 conjugacy classes — view the full character table.
| maximal subgroup of | #15693299⋊D5, #15693307⋊D5, D5×#15693303, … |
| maximal normal subgroup of | #15693299⋊D5, #15693307⋊D5, D5×#15693303, … |
| maximal quotient of | #45684413, C2×C5⋊#15693303 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16590, 44);