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C5×#15688304 #28414769

order14820
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×#15688304

Splittings

Fitting, socle, HallC5×C13×C19 ⋊ C3×C4
derived, HallC13×C19 ⋊ C3×C4×C5
HallC5×C19⋊#261 ⋊ C3
HallC5×C19×C13⋊C3 ⋊ C4
HallC19⋊#261 ⋊ C3×C5
HallC19×C13⋊C3 ⋊ C4×C5
HallC5×C13⋊C3 ⋊ Dic19
HallC5×C19 ⋊ AGL(1,𝔽13)
HallC5×C13 ⋊ C3×Dic19
HallC13⋊C3 ⋊ C5×Dic19
SylowC19 ⋊ C5×AGL(1,𝔽13)
SylowC13 ⋊ C3×C5×Dic19

Subgroups

subgroupG/H
center, hypercenterC5#15688304
commutator, hypocenterC13×C19C3×C4×C5
FrattiniC1G
Fitting, socleC5×C13×C19C3×C4
prime radicalC5×C19×D13⋊C3C2
cosocleC19×D13C2×C3×C5
LCSG ▷ C13×C19
UCSC1 ◁ C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1235

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14820, 55);