Finite Group Databasebeta

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C7×C22⋊#10625202 #35209174

order20748
automorphism?
homologyAbelianization (H1) = C3×C7 · Schur multiplier (H2) = C2

Aliases

direct productC7×C22⋊#10625202
unambiguous semidirect productC22⋊(C7×#10625202)

Splittings

Fitting, socle, HallC22×C7×C13×C19 ⋊ C3
derived, HallC22×C13×C19 ⋊ C3×C7
HallC7×C13×C19 ⋊ A4
HallC22×C7×C19 ⋊ C13⋊C3
HallC22×C7×C13 ⋊ C19⋊C3
HallC13×C19 ⋊ C7×A4
HallC7×C19 ⋊ C22⋊(C13⋊C3)
HallC7×C13 ⋊ C22⋊(C19⋊C3)
HallC22×C19 ⋊ C7×C13⋊C3
HallC22×C13 ⋊ C7×C19⋊C3
HallC22×C7 ⋊ #10625202
SylowC19 ⋊ C7×C22⋊(C13⋊C3)
SylowC13 ⋊ C7×C22⋊(C19⋊C3)
SylowC22 ⋊ C7×#10625202

Subgroups

subgroupG/H
center, hypercenterC7C22⋊#10625202
commutator, cosocle, hypocenterC22×C13×C19C3×C7
FrattiniC1G
Fitting, socleC22×C7×C13×C19C3
LCSG ▷ C22×C13×C19
UCSC1 ◁ C7

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6916

Conjugacy classes & character table

2324 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20748, 402);