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C5×#13093360⋊C2 #28414770

order14820
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×#13093360⋊C2
unambiguous semidirect product#13093360⋊(C2×C5)
unambiguous semidirect product#13093364⋊(C2×C5)
unambiguous semidirect product#13093366⋊(C2×C5)

Splittings

Fitting, socle, HallC5×C13×C19 ⋊ C22×C3
derived, HallC13×C19 ⋊ C22×C3×C5
HallC5×D13×D19 ⋊ C3
HallC5×#10625202 ⋊ C22
HallD13×D19 ⋊ C3×C5
Hall#10625202 ⋊ C22×C5
HallC5×C19 ⋊ C2×D13⋊C3
HallC5×C13 ⋊ C2×D19⋊C3
SylowC19 ⋊ C2×C5×D13⋊C3
SylowC13 ⋊ C2×C5×D19⋊C3

Subgroups

subgroupG/H
center, hypercenterC5#13093360⋊C2
commutator, cosocle, hypocenterC13×C19C22×C3×C5
FrattiniC1G
Fitting, socleC5×C13×C19C22×C3
LCSG ▷ C13×C19
UCSC1 ◁ C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1235

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14820, 56);