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C2×C11⋊(D49⋊C3) #20266282

order6468
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC2×C11⋊(D49⋊C3)
unambiguous semidirect product(C2×C11)⋊(D49⋊C3)
unambiguous semidirect product(C2×C49⋊C3)⋊D11
unambiguous semidirect product(C2×D539)⋊C3

Splittings

FittingC2×C11×C49 ⋊ C2×C3
derived, HallC11×C49 ⋊ C22×C3
HallC2×D539 ⋊ C3
HallC11×C49⋊C3 ⋊ C22
HallC49⋊C3 ⋊ C2×D11
SylowC49 ⋊ C2×C3×D11
SylowC11 ⋊ C2×D49⋊C3

Subgroups

subgroupG/H
center, hypercenterC2C11⋊(D49⋊C3)
commutator, hypocenterC11×C49C22×C3
FrattiniC7C2×C11⋊AGL(1,𝔽7)
FittingC2×C11×C49C2×C3
socleC2×C7×C11AGL(1,𝔽7)
LCSG ▷ C11×C49
UCSC1 ◁ C2

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

218 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×C11⋊(D49⋊C3), C2×C3×C11⋊(D49⋊C3), C2×C3⋊(C11⋊(D49⋊C3)), …
maximal normal subgroup ofC2×C3×C11⋊(D49⋊C3), C2×(C11⋊C5)⋊(D49⋊C3), C2×C5×C11⋊(D49⋊C3)
maximal quotient ofC2×C11⋊(D49⋊C9), D3×C11⋊(D49⋊C3), C2×C3×C11⋊(D49⋊C3), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6468, 17);