Finite Group Databasebeta

← Prev (#20259102) Next (#20259104) →

C2×C5⋊(D61⋊C5) #20259103

order6100
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5⋊(D61⋊C5)
unambiguous semidirect product(C2×C5)⋊(D61⋊C5)
unambiguous semidirect product(C2×C61⋊C5)⋊D5
unambiguous semidirect product(C2×D305)⋊C5

Splittings

Fitting, socleC2×C5×C61 ⋊ C2×C5
derivedC5×C61 ⋊ C22×C5
HallC5×C61⋊C5 ⋊ C22
SylowC61 ⋊ C2×C5×D5

Subgroups

subgroupG/H
center, hypercenterC2C5⋊(D61⋊C5)
commutator, hypocenterC5×C61C22×C5
FrattiniC1G
Fitting, socleC2×C5×C61C2×C5
LCSG ▷ C5×C61
UCSC1 ◁ C2

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

100 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C5⋊((D61⋊C3)⋊C5), D3×C5⋊(D61⋊C5), C2×C3×C5⋊(D61⋊C5), …
maximal normal subgroup ofC2×C5⋊((D61⋊C3)⋊C5), C2×C3×C5⋊(D61⋊C5)
maximal quotient ofD3×C5⋊(D61⋊C5), C2×C3×C5⋊(D61⋊C5), C2×C3⋊(C5⋊(D61⋊C5))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6100, 40);