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C5×#21439664 #50303806

order38220
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C7

Aliases

direct productC5×#21439664

Splittings

Fitting, socle, HallC5×C72×C13 ⋊ C3×C4
derived, HallC72×C13 ⋊ C3×C4×C5
HallC5×C7⋊(C7⋊#261) ⋊ C3
HallC5×C72×C13⋊C3 ⋊ C4
HallC7⋊(C7⋊#261) ⋊ C3×C5
HallC72×C13⋊C3 ⋊ C4×C5
HallC5×C72 ⋊ AGL(1,𝔽13)
HallC5×C13⋊C3 ⋊ C7⋊Dic7
HallC5×C13 ⋊ C3×C7⋊Dic7
SylowC72 ⋊ C5×AGL(1,𝔽13)
HallC13⋊C3 ⋊ C5×C7⋊Dic7
SylowC13 ⋊ C3×C5×C7⋊Dic7

Subgroups

subgroupG/H
center, hypercenterC5#21439664
commutator, hypocenterC72×C13C3×C4×C5
FrattiniC1G
Fitting, socleC5×C72×C13C3×C4
prime radicalC5×C72×D13⋊C3C2
cosocleC72×D13C2×C3×C5
LCSG ▷ C72×C13
UCSC1 ◁ C5

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3185

Conjugacy classes & character table

1025 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 492);