Finite Group Databasebeta

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C4×C7×#10625202 #35208776

order20748
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC4×C7×#10625202

Splittings

Fitting, HallC4×C7×C13×C19 ⋊ C3
derived, HallC13×C19 ⋊ C3×C4×C7
HallC7×C13×C19 ⋊ C3×C4
HallC4×C13×C19 ⋊ C3×C7
HallC4×C7×C19 ⋊ C13⋊C3
HallC4×C7×C13 ⋊ C19⋊C3
HallC7×C19 ⋊ C4×C13⋊C3
HallC7×C13 ⋊ C4×C19⋊C3
HallC4×C19 ⋊ C7×C13⋊C3
HallC4×C13 ⋊ C7×C19⋊C3
SylowC19 ⋊ C4×C7×C13⋊C3
SylowC13 ⋊ C4×C7×C19⋊C3

Subgroups

subgroupG/H
center, hypercenterC4×C7#10625202
commutator, hypocenterC13×C19C3×C4×C7
FrattiniC2C2×C7×#10625202
FittingC4×C7×C13×C19C3
socleC2×C7×C13×C19C2×C3
prime radicalC2×C7×#10625202C2
cosocleC2×C13×C19C2×C3×C7
LCSG ▷ C13×C19
UCSC1 ◁ C4×C7

48 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, 4);