Finite Group Databasebeta

← Prev (#37525653) Next (#37525655) →

C3×C7×C22⋊#63271 #37525654

order22932
automorphism?
homologyAbelianization (H1) = C32×C7 · Schur multiplier (H2) = C2×C3

Aliases

direct productC3×C7×C22⋊#63271
unambiguous semidirect product(C22×C3)⋊(C7×#63271)

Splittings

Fitting, socleC22×C3×C72×C13 ⋊ C3
derivedC22×C7×C13 ⋊ C32×C7
HallC22×C72×C13 ⋊ C32
HallC72×C13 ⋊ C3×A4
HallC22×C72 ⋊ C3×C13⋊C3
HallC22×C13 ⋊ C3×C7×ΓL(1,𝔽8)
SylowC72 ⋊ C3×C22⋊(C13⋊C3)
SylowC13 ⋊ C3×C7×C22⋊ΓL(1,𝔽8)
SylowC22 ⋊ C3×C7×#63271

Subgroups

subgroupG/H
center, hypercenterC3×C7C22⋊#63271
commutator, cosocle, hypocenterC22×C7×C13C32×C7
FrattiniC1G
Fitting, socleC22×C3×C72×C13C3
LCSG ▷ C22×C7×C13
UCSC1 ◁ C3×C7

152 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1638

Conjugacy classes & character table

2604 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22932, 1599);