Finite Group Databasebeta

← Prev (#22579612) Next (#22579614) →

C2×C3⋊(D67⋊C11) #22579613

order8844
automorphism?
homologyAbelianization (H1) = C22×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3⋊(D67⋊C11)
unambiguous semidirect product(C2×C3)⋊(D67⋊C11)
unambiguous semidirect product(C2×D201)⋊C11
unambiguous semidirect product(C2×C67⋊C11)⋊D3

Splittings

Fitting, socleC2×C3×C67 ⋊ C2×C11
derived, HallC3×C67 ⋊ C22×C11
HallC3×C67⋊C11 ⋊ C22
HallC2×D201 ⋊ C11
HallC67⋊C11 ⋊ C2×D3
SylowC67 ⋊ C2×D3×C11
SylowC3 ⋊ C2×D67⋊C11

Subgroups

subgroupG/H
center, hypercenterC2C3⋊(D67⋊C11)
commutator, hypocenterC3×C67C22×C11
FrattiniC1G
Fitting, socleC2×C3×C67C2×C11
LCSG ▷ C3×C67
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

84 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C9⋊(D67⋊C11), C2×C3⋊AGL(1,𝔽67), D3×C3⋊(D67⋊C11), …
maximal normal subgroup ofC2×C3⋊AGL(1,𝔽67), C2×C3×C3⋊(D67⋊C11)
maximal quotient ofC2×C9⋊(D67⋊C11), D3×C3⋊(D67⋊C11), C2×C3×C3⋊(D67⋊C11), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8844, 26);