Finite Group Databasebeta

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C3×C7×C22⋊#63270 #37525653

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

Aliases

direct productC3×C7×C22⋊#63270
unambiguous semidirect product(C22×C3)⋊(C7×#63270)

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×#63270

Subgroups

subgroupG/H
center, hypercenterC3×C7C22⋊#63270
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, 1598);