Finite Group Databasebeta

← Prev (#22547727) Next (#22547729) →

D5×C19×D21 #22547728

order7980
automorphism?
homologyAbelianization (H1) = C22×C19 · Schur multiplier (H2) = C2

Aliases

direct productD5×C19×D21
unambiguous semidirect product(C3×D5)⋊(D7×C19)
unambiguous semidirect product(C7×D5)⋊(D3×C19)

Splittings

Fitting, socle, HallC3×C5×C7×C19 ⋊ C22
derived, HallC3×C5×C7 ⋊ C22×C19
HallC5×C7×C19 ⋊ C2×D3
HallC3×C7×C19 ⋊ C2×D5
HallC3×C5×C19 ⋊ C2×D7
HallC7×C19 ⋊ D3×D5
HallC5×C19 ⋊ C2×D21
HallC3×C19 ⋊ D5×D7
HallC5×C7 ⋊ C2×D3×C19
HallC3×C7 ⋊ C2×D5×C19
HallC3×C5 ⋊ C2×D7×C19
SylowC7 ⋊ D3×D5×C19
SylowC5 ⋊ C2×C19×D21
SylowC3 ⋊ D5×D7×C19

Subgroups

subgroupG/H
center, hypercenterC19D5×D21
commutator, hypocenterC3×C5×C7C22×C19
FrattiniC1G
Fitting, socleC3×C5×C7×C19C22
LCSG ▷ C3×C5×C7
UCSC1 ◁ C19

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

912 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD5×C19×D63, D5×C19×C3⋊AGL(1,𝔽7), D5×C3⋊#11716325, …
maximal normal subgroup ofD5×C19×C3⋊AGL(1,𝔽7), D5×C3⋊#11716325, D5×C3⋊#11716326, …
maximal quotient ofD5×C19×D63, C3×D5×C19×D21, C19×D15×D21, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7980, 153);