Finite Group Databasebeta

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C4×C19×#63271 #35208784

order20748
automorphism?
homologyAbelianization (H1) = C3×C4×C19 · Schur multiplier (H2) = C1

Aliases

direct productC4×C19×#63271

Splittings

Fitting, HallC4×C7×C13×C19 ⋊ C3
derived, HallC7×C13 ⋊ C3×C4×C19
HallC7×C13×C19 ⋊ C3×C4
HallC4×C13×C19 ⋊ ΓL(1,𝔽8)
HallC4×C7×C19 ⋊ C13⋊C3
HallC4×C7×C13 ⋊ C3×C19
HallC13×C19 ⋊ C4×ΓL(1,𝔽8)
HallC7×C19 ⋊ C4×C13⋊C3
HallC4×C13 ⋊ C19×ΓL(1,𝔽8)
HallC4×C7 ⋊ C19×C13⋊C3
SylowC13 ⋊ C4×C19×ΓL(1,𝔽8)
SylowC7 ⋊ C4×C19×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC4×C19#63271
commutator, hypocenterC7×C13C3×C4×C19
FrattiniC2C2×C19×#63271
FittingC4×C7×C13×C19C3
socleC2×C7×C13×C19C2×C3
prime radicalC2×C19×#63271C2
cosocleC2×C7×C13C2×C3×C19
LCSG ▷ C7×C13
UCSC1 ◁ C4×C19

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6916

Conjugacy classes & character table

2508 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20748, 12);