Finite Group Databasebeta

← Prev (#36384270) Next (#36384272) →

C3×C4×C631⋊C3 #36384271

order22716
automorphism?
homologyAbelianization (H1) = C32×C4 · Schur multiplier (H2) = C3

Aliases

direct productC3×C4×C631⋊C3
unambiguous semidirect product(C4×C631)⋊C32
unambiguous semidirect product(C3×C4×C631)⋊C3

Splittings

FittingC3×C4×C631 ⋊ C3
derived, SylowC631 ⋊ C32×C4
HallC4×C631 ⋊ C32

Subgroups

subgroupG/H
center, hypercenterC3×C4C631⋊C3
commutator, hypocenterC631C32×C4
FrattiniC2C2×C3×C631⋊C3
FittingC3×C4×C631C3
socleC2×C3×C631C2×C3
prime radicalC2×C3×C631⋊C3C2
cosocleC2×C631C2×C32
LCSG ▷ C631
UCSC1 ◁ C3×C4

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7572

Conjugacy classes & character table

2556 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22716, 22);