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C2×C7×C11×D13⋊C3 #26046504

order12012
isoclinismisoclinic class of D13⋊C3
automorphism?
homologyAbelianization (H1) = C22×C3×C7×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×C7×C11×D13⋊C3
unambiguous semidirect productD13⋊(C2×C3×C7×C11)
unambiguous semidirect product(C13⋊C3)⋊(C22×C7×C11)
unambiguous semidirect product(C2×D13)⋊(C3×C7×C11)
unambiguous semidirect product(C2×C13⋊C3)⋊(C2×C7×C11)
unambiguous semidirect product(C2×C11×D13)⋊(C3×C7)

Splittings

Fitting, socleC2×C7×C11×C13 ⋊ C2×C3
derived, SylowC13 ⋊ C22×C3×C7×C11
HallC2×C7×C11×D13 ⋊ C3
HallC7×C11×C13⋊C3 ⋊ C22
HallC7×C11×C13 ⋊ C22×C3
HallC2×C11×D13 ⋊ C3×C7
HallC11×C13⋊C3 ⋊ C22×C7
HallC2×C7×D13 ⋊ C3×C11
HallC7×C13⋊C3 ⋊ C22×C11
HallC11×C13 ⋊ C22×C3×C7
HallC7×C13 ⋊ C22×C3×C11
HallC2×D13 ⋊ C3×C7×C11
HallC13⋊C3 ⋊ C22×C7×C11

Subgroups

subgroupG/H
center, hypercenterC2×C7×C11D13⋊C3
commutator, cosocle, hypocenterC13C22×C3×C7×C11
FrattiniC1G
Fitting, socleC2×C7×C11×C13C2×C3
LCSG ▷ C13
UCSC1 ◁ C2×C7×C11

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1232 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C11×ΓL(1,𝔽8)×D13⋊C3, D3×C7×C11×D13⋊C3, C2×C3×C7×C11×D13⋊C3, …
maximal normal subgroup ofC2×C11×ΓL(1,𝔽8)×D13⋊C3, C2×C3×C7×C11×D13⋊C3
maximal quotient ofC2×C7×C11×D13⋊C9, D3×C7×C11×D13⋊C3, C2×C3×C7×C11×D13⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12012, 94);