Finite Group Databasebeta

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C4×C13×C19×ΓL(1,𝔽8) #35208778

order20748
automorphism?
homologyAbelianization (H1) = C3×C4×C13×C19 · Schur multiplier (H2) = C1

Aliases

direct productC4×C13×C19×ΓL(1,𝔽8)
unambiguous semidirect product(C4×C7)⋊(C3×C13×C19)

Splittings

Fitting, HallC4×C7×C13×C19 ⋊ C3
derived, SylowC7 ⋊ C3×C4×C13×C19
HallC7×C13×C19 ⋊ C3×C4
HallC4×C7×C19 ⋊ C3×C13
HallC4×C7×C13 ⋊ C3×C19
HallC7×C19 ⋊ C3×C4×C13
HallC7×C13 ⋊ C3×C4×C19
HallC4×C7 ⋊ C3×C13×C19

Subgroups

subgroupG/H
center, hypercenterC4×C13×C19ΓL(1,𝔽8)
commutator, hypocenterC7C3×C4×C13×C19
FrattiniC2C2×C13×C19×ΓL(1,𝔽8)
FittingC4×C7×C13×C19C3
socleC2×C7×C13×C19C2×C3
prime radicalC2×C13×C19×ΓL(1,𝔽8)C2
cosocleC2×C7C2×C3×C13×C19
LCSG ▷ C7
UCSC1 ◁ C4×C13×C19

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6916

Conjugacy classes & character table

4940 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20748, 6);