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C7×C13×(C19⋊C3)⋊C4 #35208802

order20748
automorphism?
homologyAbelianization (H1) = C3×C4×C7×C13 · Schur multiplier (H2) = C1

Aliases

direct productC7×C13×(C19⋊C3)⋊C4
unambiguous semidirect product(C19⋊C3)⋊(C4×C7×C13)
unambiguous semidirect productDic19⋊(C3×C7×C13)

Splittings

derived, SylowC19 ⋊ C3×C4×C7×C13
HallC7×C13×Dic19 ⋊ C3
HallC7×C13×C19⋊C3 ⋊ C4
HallC7×C13×C19 ⋊ C3×C4
HallC13×Dic19 ⋊ C3×C7
HallC13×C19⋊C3 ⋊ C4×C7
HallC7×Dic19 ⋊ C3×C13
HallC7×C19⋊C3 ⋊ C4×C13
HallC13×C19 ⋊ C3×C4×C7
HallC7×C19 ⋊ C3×C4×C13
HallDic19 ⋊ C3×C7×C13
HallC19⋊C3 ⋊ C4×C7×C13

Subgroups

subgroupG/H
center, hypercenterC2×C7×C13D19⋊C3
commutator, hypocenterC19C3×C4×C7×C13
FrattiniC2C7×C13×D19⋊C3
Fitting, socleC2×C7×C13×C19C2×C3
prime radicalC2×C7×C13×C19⋊C3C2
cosocleC2×C19C2×C3×C7×C13
LCSG ▷ C19
UCSC1 ◁ C2×C7×C13

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6916

Conjugacy classes & character table

1638 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20748, 30);