Finite Group Databasebeta

← Prev (#21419034) Next (#21419036) →

C2×C3⋊(C11⋊(D19⋊C3)) #21419035

order7524
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3⋊(C11⋊(D19⋊C3))
unambiguous semidirect product(C2×C3)⋊(C11⋊(D19⋊C3))
unambiguous semidirect product(C2×C11)⋊(C3⋊(D19⋊C3))
unambiguous semidirect product(C2×C19⋊C3)⋊D33
unambiguous semidirect product(C2×D627)⋊C3

Splittings

Fitting, socleC2×C3×C11×C19 ⋊ C2×C3
derivedC3×C11×C19 ⋊ C22×C3
HallC3×C11×C19⋊C3 ⋊ C22
HallC11×C19 ⋊ C2×C3×D3
HallC3×C19⋊C3 ⋊ C2×D11
SylowC19 ⋊ C2×C3×D33
SylowC11 ⋊ C2×C3⋊(D19⋊C3)

Subgroups

subgroupG/H
center, hypercenterC2C3⋊(C11⋊(D19⋊C3))
commutator, hypocenterC3×C11×C19C22×C3
FrattiniC1G
Fitting, socleC2×C3×C11×C19C2×C3
LCSG ▷ C3×C11×C19
UCSC1 ◁ C2

88 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

306 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C3⋊((C11⋊C5)⋊(D19⋊C3)), D5×C3⋊(C11⋊(D19⋊C3)), C2×C5×C3⋊(C11⋊(D19⋊C3)), …
maximal normal subgroup ofC2×C3⋊((C11⋊C5)⋊(D19⋊C3)), C2×C5×C3⋊(C11⋊(D19⋊C3))
maximal quotient ofD5×C3⋊(C11⋊(D19⋊C3)), C2×C5×C3⋊(C11⋊(D19⋊C3)), C2×C3⋊(C5⋊(C11⋊(D19⋊C3)))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7524, 79);