Finite Group Databasebeta

← Prev (#26046524) Next (#26046526) →

C2×D11×#63270 #26046525

order12012
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC2×D11×#63270
unambiguous semidirect productC11⋊(C22×#63270)
unambiguous semidirect product(C2×C11)⋊(C2×#63270)

Splittings

Fitting, socleC2×C7×C11×C13 ⋊ C2×C3
derived, HallC7×C11×C13 ⋊ C22×C3
HallC2×C7×C13×D11 ⋊ C3
HallC11×#63270 ⋊ C22
HallC2×C13×D11 ⋊ ΓL(1,𝔽8)
HallC2×C7×D11 ⋊ C13⋊C3
HallC11×C13 ⋊ C22×ΓL(1,𝔽8)
HallC7×C13 ⋊ C2×C3×D11
HallC7×C11 ⋊ C22×C13⋊C3
SylowC13 ⋊ C2×ΓL(1,𝔽8)×D11
SylowC11 ⋊ C22×#63270
SylowC7 ⋊ C2×D11×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC2D11×#63270
commutator, cosocle, hypocenterC7×C11×C13C22×C3
FrattiniC1G
Fitting, socleC2×C7×C11×C13C2×C3
LCSG ▷ C7×C11×C13
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

462 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×ΓL(1,𝔽8)×D11×C13⋊C3, D3×D11×#63270, C2×C3×D11×#63270, …
maximal normal subgroup ofC2×ΓL(1,𝔽8)×D11×C13⋊C3, C2×C3×D11×#63270
maximal quotient ofC2×D11×#11717941, D3×D11×#63270, C2×C3×D11×#63270, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12012, 115);