Finite Group Databasebeta

← Prev (#22555402) Next (#22555404) →

C2×C7⋊(D61⋊C5) #22555403

order8540
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C7⋊(D61⋊C5)
unambiguous semidirect product(C2×C7)⋊(D61⋊C5)
unambiguous semidirect product(C2×C61⋊C5)⋊D7
unambiguous semidirect product(C2×D427)⋊C5

Splittings

Fitting, socleC2×C7×C61 ⋊ C2×C5
derived, HallC7×C61 ⋊ C22×C5
HallC7×C61⋊C5 ⋊ C22
HallC2×D427 ⋊ C5
HallC61⋊C5 ⋊ C2×D7
SylowC61 ⋊ C2×C5×D7
SylowC7 ⋊ C2×D61⋊C5

Subgroups

subgroupG/H
center, hypercenterC2C7⋊(D61⋊C5)
commutator, hypocenterC7×C61C22×C5
FrattiniC1G
Fitting, socleC2×C7×C61C2×C5
LCSG ▷ C7×C61
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

134 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#14579429⋊C5, C2×#14579428⋊C5, C2×ΓL(1,𝔽8)⋊(D61⋊C5), …
maximal normal subgroup ofC2×#14579429⋊C5, C2×#14579428⋊C5, C2×ΓL(1,𝔽8)⋊(D61⋊C5), …
maximal quotient ofD3×C7⋊(D61⋊C5), C2×C3×C7⋊(D61⋊C5), C2×C3⋊(C7⋊(D61⋊C5))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8540, 18);