Finite Group Databasebeta

← Prev (#43244874) Next (#43244876) →

C5×#14584195⋊C2 #43244875

order28140
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×#14584195⋊C2
unambiguous semidirect product#14584195⋊(C2×C5)
unambiguous semidirect product#14584199⋊(C2×C5)
unambiguous semidirect product#14584203⋊(C2×C5)

Splittings

Fitting, socle, HallC5×C7×C67 ⋊ C22×C3
derived, HallC7×C67 ⋊ C22×C3×C5
HallC5×D7×D67 ⋊ C3
HallC5×#13064105 ⋊ C22
HallD7×D67 ⋊ C3×C5
Hall#13064105 ⋊ C22×C5
HallC5×C67 ⋊ C2×AGL(1,𝔽7)
SylowC67 ⋊ C2×C5×AGL(1,𝔽7)
HallC5×C7 ⋊ C2×D67⋊C3
SylowC7 ⋊ C2×C5×D67⋊C3

Subgroups

subgroupG/H
center, hypercenterC5#14584195⋊C2
commutator, cosocle, hypocenterC7×C67C22×C3×C5
FrattiniC1G
Fitting, socleC5×C7×C67C22×C3
LCSG ▷ C7×C67
UCSC1 ◁ C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2345

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28140, 51);