Finite Group DatabasebetaFinite Group Databasebeta| order | 17670 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊#16812976 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C19×C31 | C2×C3 |
| LCS | G ▷ C5×C19×C31 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2945 |
Polycyclic presentation:
2,3,5,19,31|c^a=c^4,d^a=d^18,e^a=e^30,d^b=d^7,e^b=e^5502 conjugacy classes — view the full character table.
| maximal subgroup of | #16812968⋊D5, #16812972⋊D5, D5×#16812976, … |
| maximal normal subgroup of | #16812968⋊D5, #16812972⋊D5, D5×#16812976, … |
| maximal quotient of | #47977588, C2×C5⋊#16812976 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17670, 60);