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C11×D7×D13⋊C3 #26046497

order12012
automorphism?
homologyAbelianization (H1) = C22×C3×C11 · Schur multiplier (H2) = C2

Aliases

direct productC11×D7×D13⋊C3
unambiguous semidirect productD13⋊(C3×C11×D7)
unambiguous semidirect product(C7×D13⋊C3)⋊(C2×C11)
unambiguous semidirect product(D7×C13⋊C3)⋊(C2×C11)
unambiguous semidirect product((C13⋊C3)⋊D7)⋊(C2×C11)

Splittings

Fitting, socle, HallC7×C11×C13 ⋊ C22×C3
derived, HallC7×C13 ⋊ C22×C3×C11
HallC11×D7×D13 ⋊ C3
HallC7×C11×C13⋊C3 ⋊ C22
HallC11×C13⋊C3 ⋊ C2×D7
HallD7×D13 ⋊ C3×C11
HallC7×C13⋊C3 ⋊ C22×C11
HallC11×C13 ⋊ C2×C3×D7
HallC7×C11 ⋊ C2×D13⋊C3
HallC13⋊C3 ⋊ C2×C11×D7
SylowC13 ⋊ C2×C3×C11×D7
SylowC7 ⋊ C2×C11×D13⋊C3

Subgroups

subgroupG/H
center, hypercenterC11D7×D13⋊C3
commutator, cosocle, hypocenterC7×C13C22×C3×C11
FrattiniC1G
Fitting, socleC7×C11×C13C22×C3
LCSG ▷ C7×C13
UCSC1 ◁ C11

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

440 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC11×AGL(1,𝔽7)×D13⋊C3, C3×C11×D7×D13⋊C3, C11×D21×D13⋊C3, …
maximal normal subgroup ofC11×AGL(1,𝔽7)×D13⋊C3, C3×C11×D7×D13⋊C3
maximal quotient ofC11×D7×D13⋊C9, C3×C11×D7×D13⋊C3, C11×D21×D13⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12012, 87);