Finite Group Databasebeta

← Prev (#22547753) Next (#22547755) →

C2×C5×C19×D21 #22547754

order7980
isoclinismisoclinic class of D21
automorphism?
homologyAbelianization (H1) = C22×C5×C19 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C19×D21
unambiguous semidirect product(C2×C3)⋊(C5×D7×C19)
unambiguous semidirect product(C2×C7)⋊(C5×D3×C19)

Splittings

Fitting, socleC2×C3×C5×C7×C19 ⋊ C2
derived, HallC3×C7 ⋊ C22×C5×C19
HallC3×C5×C7×C19 ⋊ C22
HallC5×C7×C19 ⋊ C2×D3
HallC3×C7×C19 ⋊ C22×C5
HallC3×C5×C19 ⋊ C2×D7
HallC7×C19 ⋊ C2×C5×D3
HallC3×C5×C7 ⋊ C22×C19
HallC3×C19 ⋊ C2×C5×D7
HallC5×C7 ⋊ C2×D3×C19
HallC3×C5 ⋊ C2×D7×C19
SylowC7 ⋊ C2×C5×D3×C19
SylowC3 ⋊ C2×C5×D7×C19

Subgroups

subgroupG/H
center, hypercenterC2×C5×C19D21
commutator, hypocenterC3×C7C22×C5×C19
FrattiniC1G
Fitting, socleC2×C3×C5×C7×C19C2
LCSG ▷ C3×C7
UCSC1 ◁ C2×C5×C19

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2280 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C5×C19×D63, C2×C5×C19×C3⋊AGL(1,𝔽7), C2×C5×C3⋊#11716325, …
maximal normal subgroup ofC2×C5×C19×C3⋊AGL(1,𝔽7), C2×C5×C3⋊#11716325, C2×C5×C3⋊#11716326, …
maximal quotient ofC2×C5×C19×D63, C5×D3×C19×D21, C2×C3×C5×C19×D21, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7980, 179);