Finite Group Databasebeta

← Prev (#26046522) Next (#26046524) →

C2×C11⋊#10587716 #26046523

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

Aliases

direct productC2×C11⋊#10587716
unambiguous semidirect product(C2×C11)⋊#10587716

Splittings

Fitting, socleC2×C7×C11×C13 ⋊ C2×C3
derived, HallC7×C11×C13 ⋊ C22×C3
HallC2×C7×D143 ⋊ C3
HallC11×#63270 ⋊ C22
HallC2×D143 ⋊ ΓL(1,𝔽8)
Hall#63270 ⋊ C2×D11
HallC11×C13 ⋊ C22×ΓL(1,𝔽8)
HallC7×C13 ⋊ C2×C3×D11
HallC7×C11 ⋊ C2×D13⋊C3
SylowC13 ⋊ C2×ΓL(1,𝔽8)×D11
SylowC11 ⋊ C2×#10587716
SylowC7 ⋊ C2×C11⋊(D13⋊C3)

Subgroups

subgroupG/H
center, hypercenterC2C11⋊#10587716
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

378 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×ΓL(1,𝔽8)×C11⋊(D13⋊C3), D3×C11⋊#10587716, C2×C3×C11⋊#10587716, …
maximal normal subgroup ofC2×ΓL(1,𝔽8)×C11⋊(D13⋊C3), C2×C3×C11⋊#10587716
maximal quotient ofC2×C11⋊#13109896, D3×C11⋊#10587716, C2×C3×C11⋊#10587716, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12012, 113);