Finite Group Databasebeta

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C13×#11758266⋊C3 #50303820

order38220
automorphism?
homologyAbelianization (H1) = C3×C4×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×#11758266⋊C3
unambiguous semidirect product#11758266⋊(C3×C13)

Splittings

Fitting, socle, HallC5×C72×C13 ⋊ C3×C4
derived, HallC5×C72 ⋊ C3×C4×C13
HallC13×#11758266 ⋊ C3
HallC5×C13×#3861 ⋊ C4
HallC13×#3861 ⋊ AGL(1,𝔽5)
Hall#11758266 ⋊ C3×C13
HallC5×#3861 ⋊ C4×C13
HallC72×C13 ⋊ C3×AGL(1,𝔽5)
Hall#3861 ⋊ C13×AGL(1,𝔽5)
HallC5×C13 ⋊ #5997⋊C3
SylowC72 ⋊ C3×C13×AGL(1,𝔽5)
SylowC5 ⋊ C13×#5997⋊C3

Subgroups

subgroupG/H
center, hypercenterC13#11758266⋊C3
commutator, hypocenterC5×C72C3×C4×C13
FrattiniC1G
Fitting, socleC5×C72×C13C3×C4
prime radicalC13×C5⋊#64424C2
cosocleC5⋊(C7⋊D7)C2×C3×C13
LCSG ▷ C5×C72
UCSC1 ◁ C13

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 910

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 506);