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C22×C7×#10625202 #35209187

order20748
automorphism?
homologyAbelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2

Aliases

direct productC22×C7×#10625202

Splittings

Fitting, socle, HallC22×C7×C13×C19 ⋊ C3
derived, HallC13×C19 ⋊ C22×C3×C7
HallC7×C13×C19 ⋊ C22×C3
HallC22×C13×C19 ⋊ C3×C7
HallC22×C7×C19 ⋊ C13⋊C3
HallC22×C7×C13 ⋊ C19⋊C3
HallC7×C19 ⋊ C22×C13⋊C3
HallC7×C13 ⋊ C22×C19⋊C3
HallC22×C19 ⋊ C7×C13⋊C3
HallC22×C13 ⋊ C7×C19⋊C3
SylowC19 ⋊ C22×C7×C13⋊C3
SylowC13 ⋊ C22×C7×C19⋊C3

Subgroups

subgroupG/H
center, hypercenterC22×C7#10625202
commutator, cosocle, hypocenterC13×C19C22×C3×C7
FrattiniC1G
Fitting, socleC22×C7×C13×C19C3
LCSG ▷ C13×C19
UCSC1 ◁ C22×C7

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6916

Conjugacy classes & character table

2380 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20748, 415);