Finite Group Databasebeta

← Prev (#32912996) Next (#32912998) →

C2×C5⋊((D61⋊C3)⋊C5) #32912997

order18300
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5⋊((D61⋊C3)⋊C5)
unambiguous semidirect product(C2×C5)⋊((D61⋊C3)⋊C5)
unambiguous semidirect product(C2×(C61⋊C3)⋊C5)⋊D5
unambiguous semidirect product(C2×C5⋊(D61⋊C3))⋊C5
unambiguous semidirect product(C2×C5⋊(D61⋊C5))⋊C3

Splittings

Fitting, socleC2×C5×C61 ⋊ C2×C3×C5
derivedC5×C61 ⋊ C22×C3×C5
HallC2×C5⋊(D61⋊C5) ⋊ C3
HallC5×(C61⋊C3)⋊C5 ⋊ C22
HallC5×C61⋊C5 ⋊ C22×C3
HallC61⋊C3 ⋊ C2×C5×D5
SylowC61 ⋊ C2×C3×C5×D5

Subgroups

subgroupG/H
center, hypercenterC2C5⋊((D61⋊C3)⋊C5)
commutator, cosocle, hypocenterC5×C61C22×C3×C5
FrattiniC1G
Fitting, socleC2×C5×C61C2×C3×C5
LCSG ▷ C5×C61
UCSC1 ◁ C2

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 610

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18300, 120);