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C2×C3×C7×D143 #26046596

order12012
isoclinismisoclinic class of D143
automorphism?
homologyAbelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C7×D143
unambiguous semidirect product(C2×C11)⋊(C3×C7×D13)

Splittings

Fitting, socleC2×C3×C7×C11×C13 ⋊ C2
derived, HallC11×C13 ⋊ C22×C3×C7
HallC3×C7×C11×C13 ⋊ C22
HallC7×C11×C13 ⋊ C22×C3
HallC3×C11×C13 ⋊ C22×C7
HallC3×C7×C13 ⋊ C2×D11
HallC3×C7×C11 ⋊ C2×D13
HallC7×C13 ⋊ C2×C3×D11
HallC7×C11 ⋊ C2×C3×D13
HallC3×C13 ⋊ C2×C7×D11
HallC3×C11 ⋊ C2×C7×D13
SylowC13 ⋊ C2×C3×C7×D11
SylowC11 ⋊ C2×C3×C7×D13

Subgroups

subgroupG/H
center, hypercenterC2×C3×C7D143
commutator, cosocle, hypocenterC11×C13C22×C3×C7
FrattiniC1G
Fitting, socleC2×C3×C7×C11×C13C2
LCSG ▷ C11×C13
UCSC1 ◁ C2×C3×C7

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3066 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C7×C11⋊(D13⋊C9), C2×C11⋊#13109896, C2×C11⋊#13109897, …
maximal normal subgroup ofC2×C7×C11⋊(D13⋊C9), C2×C11⋊#13109896, C2×C11⋊#13109897, …
maximal quotient ofC2×C7×C9×D143, C3×D3×C7×D143, C2×C32×C7×D143, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12012, 186);