Finite Group Databasebeta

← Prev (#26046469) Next (#26046471) →

D11×#10587722 #26046470

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

Aliases

direct productD11×#10587722

Splittings

Fitting, socle, derived, HallC7×C11×C13 ⋊ C22×C3
HallD11×D91 ⋊ C3
HallC11×#63270 ⋊ C22
Hall#63270 ⋊ C2×D11
HallC11×C13 ⋊ C2×AGL(1,𝔽7)
HallC7×C13 ⋊ C2×C3×D11
HallC7×C11 ⋊ C2×D13⋊C3
SylowC13 ⋊ D11×AGL(1,𝔽7)
SylowC11 ⋊ C2×#10587722
SylowC7 ⋊ D11×D13⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C11×C13C22×C3
LCSG ▷ C7×C11×C13
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

147 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD11×ΓL(1,𝔽8)⋊(D13⋊C3), C3×D11×#10587722, D11×C3⋊#10587722, …
maximal normal subgroup ofD11×ΓL(1,𝔽8)⋊(D13⋊C3), C3×D11×#10587722
maximal quotient ofD11×#13109902, C3×D11×#10587722, D11×C3⋊#10587722, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12012, 60);