Finite Group Databasebeta

C2×C31×D31⋊C9 #46829311

order34596
automorphism?
homologyAbelianization (H1) = C22×C9×C31 · Schur multiplier (H2) = C2

Aliases

direct productC2×C31×D31⋊C9
unambiguous semidirect productD31⋊(C2×C9×C31)
unambiguous semidirect product(C2×D31)⋊(C9×C31)
unambiguous semidirect product(C31⋊C9)⋊(C22×C31)
unambiguous semidirect product(C2×C31⋊C9)⋊(C2×C31)

Splittings

derivedC31 ⋊ C22×C9×C31
HallC31×C31⋊C9 ⋊ C22
HallC2×C31×D31 ⋊ C9
SylowC312 ⋊ C22×C9

Subgroups

subgroupG/H
center, hypercenterC2×C3×C31D31⋊C3
commutator, hypocenterC31C22×C9×C31
FrattiniC3C2×C31×D31⋊C3
Fitting, socleC2×C3×C312C2×C3
prime radicalC2×C3×C31×D31C3
cosocleC3×C31C22×C3×C31
LCSG ▷ C31
UCSC1 ◁ C2×C3×C31

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1116

Conjugacy classes & character table

2046 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34596, 71);