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C19×C3⋊(C7⋊#261) #35209148

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

Aliases

direct productC19×C3⋊(C7⋊#261)
unambiguous semidirect productC3⋊(C19×C7⋊#261)
unambiguous semidirect productC7⋊(C19×C3⋊#261)

Splittings

Fitting, socle, HallC3×C7×C13×C19 ⋊ C4
derived, HallC3×C7×C13 ⋊ C4×C19
HallC7×C13×C19 ⋊ Dic3
HallC3×C13×C19 ⋊ Dic7
HallC3×C7×C19 ⋊ #261
HallC13×C19 ⋊ Dic21
HallC7×C19 ⋊ C3⋊#261
HallC7×C13 ⋊ Dic3×C19
HallC3×C19 ⋊ C7⋊#261
HallC3×C13 ⋊ C19×Dic7
HallC3×C7 ⋊ C19×#261
SylowC13 ⋊ C19×Dic21
SylowC7 ⋊ C19×C3⋊#261
SylowC3 ⋊ C19×C7⋊#261

Subgroups

subgroupG/H
center, hypercenterC19C3⋊(C7⋊#261)
commutator, hypocenterC3×C7×C13C4×C19
FrattiniC1G
Fitting, socleC3×C7×C13×C19C4
prime radicalC3×C7×C19×D13C2
cosocleC3×C7×D13C2×C19
LCSG ▷ C3×C7×C13
UCSC1 ◁ C19

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5187

Conjugacy classes & character table

1653 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20748, 376);