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C2×C13×D231 #26046585

order12012
isoclinismisoclinic class of D231
automorphism?
homologyAbelianization (H1) = C22×C13 · Schur multiplier (H2) = C2

Aliases

direct productC2×C13×D231
unambiguous semidirect product(C2×C3)⋊(C13×D77)
unambiguous semidirect product(C2×C7)⋊(C13×D33)
unambiguous semidirect product(C2×C11)⋊(C13×D21)

Splittings

Fitting, socleC2×C3×C7×C11×C13 ⋊ C2
derived, HallC3×C7×C11 ⋊ C22×C13
HallC3×C7×C11×C13 ⋊ C22
HallC7×C11×C13 ⋊ C2×D3
HallC3×C11×C13 ⋊ C2×D7
HallC3×C7×C13 ⋊ C2×D11
HallC11×C13 ⋊ C2×D21
HallC7×C13 ⋊ C2×D33
HallC7×C11 ⋊ C2×D3×C13
HallC3×C13 ⋊ C2×D77
HallC3×C11 ⋊ C2×C13×D7
HallC3×C7 ⋊ C2×C13×D11
SylowC11 ⋊ C2×C13×D21
SylowC7 ⋊ C2×C13×D33
SylowC3 ⋊ C2×C13×D77

Subgroups

subgroupG/H
center, hypercenterC2×C13D231
commutator, cosocle, hypocenterC3×C7×C11C22×C13
FrattiniC1G
Fitting, socleC2×C3×C7×C11×C13C2
LCSG ▷ C3×C7×C11
UCSC1 ◁ C2×C13

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3042 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C13×D693, C2×C13×C3⋊(C11⋊AGL(1,𝔽7)), C2×C3⋊(C11⋊#10587720), …
maximal normal subgroup ofC2×C13×C3⋊(C11⋊AGL(1,𝔽7)), C2×C3⋊(C11⋊#10587720), C2×C3⋊(C11⋊#10587721), …
maximal quotient ofC2×C13×D693, D3×C13×D231, C2×C3×C13×D231, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12012, 175);