Finite Group Databasebeta

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C2×D3×C7×C11×C13 #26046591

order12012
isoclinismisoclinic class of D3
automorphism?
homologyAbelianization (H1) = C22×C7×C11×C13 · Schur multiplier (H2) = C2

Aliases

direct productC2×D3×C7×C11×C13
unambiguous semidirect productC3⋊(C22×C7×C11×C13)
unambiguous semidirect product(C2×C3)⋊(C2×C7×C11×C13)

Splittings

Fitting, socleC2×C3×C7×C11×C13 ⋊ C2
derived, SylowC3 ⋊ C22×C7×C11×C13
HallC3×C7×C11×C13 ⋊ C22
HallC3×C11×C13 ⋊ C22×C7
HallC3×C7×C13 ⋊ C22×C11
HallC3×C7×C11 ⋊ C22×C13
HallC3×C13 ⋊ C22×C7×C11
HallC3×C11 ⋊ C22×C7×C13
HallC3×C7 ⋊ C22×C11×C13

Subgroups

subgroupG/H
center, hypercenterC2×C7×C11×C13D3
commutator, cosocle, hypocenterC3C22×C7×C11×C13
FrattiniC1G
Fitting, socleC2×C3×C7×C11×C13C2
LCSG ▷ C3
UCSC1 ◁ C2×C7×C11×C13

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6006 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C7×C11×C13×D9, C2×D3×C7×C11×C13⋊C3, C2×D3×C11×C13×ΓL(1,𝔽8), …
maximal normal subgroup ofC2×D3×C7×C11×C13⋊C3, C2×D3×C11×C13×ΓL(1,𝔽8), C2×D3×C11×#63270, …
maximal quotient ofC2×C7×C11×C13×D9, D32×C7×C11×C13, C2×C3×D3×C7×C11×C13, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12012, 181);