Finite Group Databasebeta

← Prev (#22547685) Next (#22547687) →

C2×C5⋊#11716325 #22547686

order7980
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5⋊#11716325
unambiguous semidirect product(C2×C5)⋊#11716325

Splittings

Fitting, socleC2×C5×C7×C19 ⋊ C2×C3
derived, HallC5×C7×C19 ⋊ C22×C3
HallC2×C19×D35 ⋊ C3
HallC5×#87704 ⋊ C22
Hall#87704 ⋊ C2×D5
HallC2×D35 ⋊ C19⋊C3
HallC7×C19 ⋊ C2×C3×D5
HallC5×C19 ⋊ C2×AGL(1,𝔽7)
HallC5×C7 ⋊ C22×C19⋊C3
SylowC19 ⋊ C2×C5⋊AGL(1,𝔽7)
SylowC7 ⋊ C2×D5×C19⋊C3
SylowC5 ⋊ C2×#11716325

Subgroups

subgroupG/H
center, hypercenterC2C5⋊#11716325
commutator, hypocenterC5×C7×C19C22×C3
FrattiniC1G
Fitting, socleC2×C5×C7×C19C2×C3
LCSG ▷ C5×C7×C19
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

262 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C19⋊C3×C5⋊AGL(1,𝔽7), D3×C5⋊#11716325, C2×C3×C5⋊#11716325, …
maximal normal subgroup ofC2×C19⋊C3×C5⋊AGL(1,𝔽7), C2×C3×C5⋊#11716325
maximal quotient ofC2×C5⋊#14558784, D3×C5⋊#11716325, C2×C3×C5⋊#11716325, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7980, 111);