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C2×C3×AGL(1,𝔽67) #40997652

order26532
automorphism?
homologyAbelianization (H1) = C22×C32×C11 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C3×AGL(1,𝔽67)
unambiguous semidirect product(D67⋊C3)⋊(C2×C3×C11)
unambiguous semidirect product(C2×D67⋊C3)⋊(C3×C11)
unambiguous semidirect product(D67⋊C11)⋊(C2×C32)
unambiguous semidirect product((C67⋊C3)⋊C11)⋊(C22×C3)
unambiguous semidirect product(C2×C3×D67⋊C3)⋊C11
unambiguous semidirect product(C2×D67⋊C11)⋊C32
unambiguous semidirect product(C2×(C67⋊C3)⋊C11)⋊(C2×C3)
unambiguous semidirect product(C2×C3×D67⋊C11)⋊C3

Splittings

Fitting, socleC2×C3×C67 ⋊ C2×C3×C11
derived, SylowC67 ⋊ C22×C32×C11
HallC3×(C67⋊C3)⋊C11 ⋊ C22
HallC2×D67⋊C11 ⋊ C32
HallC2×C3×D67⋊C3 ⋊ C11
HallC67⋊C11 ⋊ C22×C32
HallC3×C67⋊C3 ⋊ C22×C11
HallC2×D67 ⋊ C32×C11

Subgroups

subgroupG/H
center, hypercenterC2×C3AGL(1,𝔽67)
commutator, cosocle, hypocenterC67C22×C32×C11
FrattiniC1G
Fitting, socleC2×C3×C67C2×C3×C11
LCSG ▷ C67
UCSC1 ◁ C2×C3

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 402

Conjugacy classes & character table

402 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26532, 83);