Finite Group Databasebeta

← Prev (#46829295) Next (#46829297) →

C4×C31×C31⋊C9 #46829296

order34596
automorphism?
homologyAbelianization (H1) = C4×C9×C31 · Schur multiplier (H2) = C1

Aliases

direct productC4×C31×C31⋊C9
unambiguous semidirect product(C4×C31)⋊(C9×C31)

Splittings

derivedC31 ⋊ C4×C9×C31
HallC4×C312 ⋊ C9
SylowC312 ⋊ C4×C9

Subgroups

subgroupG/H
center, hypercenterC3×C4×C31C31⋊C3
commutator, hypocenterC31C4×C9×C31
FrattiniC2×C3C2×C31×C31⋊C3
FittingC3×C4×C312C3
socle, prime radicalC2×C3×C312C2×C3
cosocleC2×C3×C31C2×C3×C31
LCSG ▷ C31
UCSC1 ◁ C3×C4×C31

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1116

Conjugacy classes & character table

4836 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34596, 56);