Finite Group Databasebeta

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C7×C13⋊C3×Dic19 #35208803

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

Aliases

direct productC7×C13⋊C3×Dic19

Splittings

derived, HallC13×C19 ⋊ C3×C4×C7
HallC7×C13×Dic19 ⋊ C3
HallC7×C19×C13⋊C3 ⋊ C4
HallC7×C13×C19 ⋊ C3×C4
HallC13×Dic19 ⋊ C3×C7
HallC19×C13⋊C3 ⋊ C4×C7
HallC7×C19 ⋊ C4×C13⋊C3
HallC7×C13 ⋊ C3×Dic19
SylowC19 ⋊ C4×C7×C13⋊C3
SylowC13 ⋊ C3×C7×Dic19

Subgroups

subgroupG/H
center, hypercenterC2×C7D19×C13⋊C3
commutator, hypocenterC13×C19C3×C4×C7
FrattiniC2C7×D19×C13⋊C3
Fitting, socleC2×C7×C13×C19C2×C3
prime radicalC2×C7×C19×C13⋊C3C2
cosocleC2×C13×C19C2×C3×C7
LCSG ▷ C13×C19
UCSC1 ◁ C2×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6916

Conjugacy classes & character table

1078 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20748, 31);