Finite Group Databasebeta

← Prev (#23778355) Next (#23778357) →

C5×#10621721⋊C3 #23778356

order10140
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×#10621721⋊C3
unambiguous semidirect product#10621721⋊(C3×C5)
unambiguous semidirect product(C5×#10621721)⋊C3

Splittings

Fitting, HallC5×C169 ⋊ C3×C4
derived, SylowC169 ⋊ C3×C4×C5
HallC5×#10621721 ⋊ C3
HallC5×C169⋊C3 ⋊ C4
Hall#10621721 ⋊ C3×C5
HallC169⋊C3 ⋊ C4×C5

Subgroups

subgroupG/H
center, hypercenterC5#10621721⋊C3
commutator, hypocenterC169C3×C4×C5
FrattiniC13C5×AGL(1,𝔽13)
FittingC5×C169C3×C4
socleC5×C13AGL(1,𝔽13)
prime radicalC5×D169⋊C3C2
cosocleD169C2×C3×C5
LCSG ▷ C169
UCSC1 ◁ C5

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

130 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C5×#10621721⋊C3, C5×C3⋊(#10621721⋊C3)
maximal normal subgroup ofC3×C5×#10621721⋊C3
maximal quotient ofC5×#10621721⋊C9, C3×C5×#10621721⋊C3, C5×C3⋊(#10621721⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10140, 14);