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C11×D7×D39 #26046560

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

Aliases

direct productC11×D7×D39
unambiguous semidirect product(C3×D7)⋊(C11×D13)
unambiguous semidirect product(C13×D7)⋊(D3×C11)

Splittings

Fitting, socle, HallC3×C7×C11×C13 ⋊ C22
derived, HallC3×C7×C13 ⋊ C22×C11
HallC7×C11×C13 ⋊ C2×D3
HallC3×C11×C13 ⋊ C2×D7
HallC3×C7×C11 ⋊ C2×D13
HallC11×C13 ⋊ D3×D7
HallC7×C13 ⋊ C2×D3×C11
HallC7×C11 ⋊ C2×D39
HallC3×C13 ⋊ C2×C11×D7
HallC3×C11 ⋊ D7×D13
HallC3×C7 ⋊ C2×C11×D13
SylowC13 ⋊ D3×C11×D7
SylowC7 ⋊ C2×C11×D39
SylowC3 ⋊ C11×D7×D13

Subgroups

subgroupG/H
center, hypercenterC11D7×D39
commutator, cosocle, hypocenterC3×C7×C13C22×C11
FrattiniC1G
Fitting, socleC3×C7×C11×C13C22
LCSG ▷ C3×C7×C13
UCSC1 ◁ C11

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1155 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC11×D7×D117, C11×#10587720⋊D3, C11×#10587721⋊D3, …
maximal normal subgroup ofC11×#10587720⋊D3, C11×#10587721⋊D3, C11×AGL(1,𝔽7)×D39, …
maximal quotient ofC11×D7×D117, C3×C11×D7×D39, C11×D21×D39, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12012, 150);