Finite Group Databasebeta

D3×C31×C169 #44537612

order31434
automorphism?
homologyAbelianization (H1) = C2×C31×C169 · Schur multiplier (H2) = C1

Aliases

direct productD3×C31×C169
unambiguous semidirect productC3⋊(C2×C31×C169)

Splittings

Fitting, HallC3×C31×C169 ⋊ C2
derived, SylowC3 ⋊ C2×C31×C169
HallC3×C169 ⋊ C2×C31
HallC3×C31 ⋊ C2×C169

Subgroups

subgroupG/H
center, hypercenterC31×C169D3
commutator, hypocenterC3C2×C31×C169
FrattiniC13D3×C13×C31
FittingC3×C31×C169C2
socleC3×C13×C31C2×C13
prime radicalD3×C13×C31C13
cosocleC3×C13C2×C13×C31
LCSG ▷ C3
UCSC1 ◁ C31×C169

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15717

Conjugacy classes & character table

15717 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31434, 9);