Finite Group Databasebeta

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C2×C5×D67⋊C11 #28413907

order14740
automorphism?
homologyAbelianization (H1) = C22×C5×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×D67⋊C11
unambiguous semidirect productD67⋊(C2×C5×C11)
unambiguous semidirect product(C2×D67)⋊(C5×C11)
unambiguous semidirect product(C67⋊C11)⋊(C22×C5)
unambiguous semidirect product(C2×C5×D67)⋊C11
unambiguous semidirect product(C2×C67⋊C11)⋊(C2×C5)

Splittings

Fitting, socleC2×C5×C67 ⋊ C2×C11
derived, SylowC67 ⋊ C22×C5×C11
HallC5×C67⋊C11 ⋊ C22
HallC2×C5×D67 ⋊ C11
HallC67⋊C11 ⋊ C22×C5
HallC5×C67 ⋊ C22×C11
HallC2×D67 ⋊ C5×C11

Subgroups

subgroupG/H
center, hypercenterC2×C5D67⋊C11
commutator, cosocle, hypocenterC67C22×C5×C11
FrattiniC1G
Fitting, socleC2×C5×C67C2×C11
LCSG ▷ C67
UCSC1 ◁ C2×C5

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 670

Conjugacy classes & character table

250 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14740, 21);