Finite Group Databasebeta

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C5×#13095532⋊C2 #29509552

order15540
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×#13095532⋊C2
unambiguous semidirect product#13095532⋊(C2×C5)
unambiguous semidirect product#13095536⋊(C2×C5)
unambiguous semidirect product#13095538⋊(C2×C5)

Splittings

Fitting, socle, HallC5×C7×C37 ⋊ C22×C3
derived, HallC7×C37 ⋊ C22×C3×C5
HallC5×D7×D37 ⋊ C3
HallC5×#11715912 ⋊ C22
HallD7×D37 ⋊ C3×C5
Hall#11715912 ⋊ C22×C5
HallC5×C37 ⋊ C2×AGL(1,𝔽7)
SylowC37 ⋊ C2×C5×AGL(1,𝔽7)
HallC5×C7 ⋊ C2×D37⋊C3
SylowC7 ⋊ C2×C5×D37⋊C3

Subgroups

subgroupG/H
center, hypercenterC5#13095532⋊C2
commutator, cosocle, hypocenterC7×C37C22×C3×C5
FrattiniC1G
Fitting, socleC5×C7×C37C22×C3
LCSG ▷ C7×C37
UCSC1 ◁ C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1295

Conjugacy classes & character table

220 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15540, 54);