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C13×#15668765 #50303900

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

Aliases

direct productC13×#15668765

Splittings

Fitting, socle, HallC5×C72×C13 ⋊ C3×C4
derived, HallC5×C72 ⋊ C3×C4×C13
HallC13×C7⋊(C7⋊AGL(1,𝔽5)) ⋊ C3
HallC5×C13×#3861 ⋊ C4
HallC13×#3861 ⋊ AGL(1,𝔽5)
HallC7⋊(C7⋊AGL(1,𝔽5)) ⋊ C3×C13
HallC5×#3861 ⋊ C4×C13
HallC72×C13 ⋊ C3×AGL(1,𝔽5)
Hall#3861 ⋊ C13×AGL(1,𝔽5)
HallC5×C13 ⋊ #10596874
SylowC72 ⋊ C3×C13×AGL(1,𝔽5)
SylowC5 ⋊ C13×#10596874

Subgroups

subgroupG/H
center, hypercenterC13#15668765
commutator, hypocenterC5×C72C3×C4×C13
FrattiniC1G
Fitting, socleC5×C72×C13C3×C4
prime radicalD5×C13×#3861C2
cosocleC72×D5C2×C3×C13
LCSG ▷ C5×C72
UCSC1 ◁ C13

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3185

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 586);