Finite Group Databasebeta

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C13×#13097583 #35208808

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

Aliases

direct productC13×#13097583

Splittings

derived, HallC7×C19 ⋊ C3×C4×C13
HallC7×C13×Dic19 ⋊ C3
HallC13×#87705 ⋊ C4
HallC7×C13×C19 ⋊ C3×C4
HallC13×Dic19 ⋊ ΓL(1,𝔽8)
HallC7×Dic19 ⋊ C3×C13
Hall#87705 ⋊ C4×C13
HallC13×C19 ⋊ C4×ΓL(1,𝔽8)
HallC7×C13 ⋊ (C19⋊C3)⋊C4
HallDic19 ⋊ C13×ΓL(1,𝔽8)
SylowC19 ⋊ C4×C13×ΓL(1,𝔽8)
SylowC7 ⋊ C13×(C19⋊C3)⋊C4

Subgroups

subgroupG/H
center, hypercenterC2×C13#11716322
commutator, hypocenterC7×C19C3×C4×C13
FrattiniC2C13×#11716322
Fitting, socleC2×C7×C13×C19C2×C3
prime radicalC2×C13×#87705C2
cosocleC2×C7×C19C2×C3×C13
LCSG ▷ C7×C19
UCSC1 ◁ C2×C13

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6916

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20748, 36);