Finite Group Databasebeta

← Prev (#26046551) Next (#26046553) →

C11×D13×D21 #26046552

order12012
automorphism?
homologyAbelianization (H1) = C22×C11 · Schur multiplier (H2) = C2

Aliases

direct productC11×D13×D21
unambiguous semidirect product(C3×D13)⋊(C11×D7)
unambiguous semidirect product(C7×D13)⋊(D3×C11)

Splittings

Fitting, socle, HallC3×C7×C11×C13 ⋊ C22
derived, HallC3×C7×C13 ⋊ C22×C11
HallC7×C11×C13 ⋊ C2×D3
HallC3×C11×C13 ⋊ C2×D7
HallC3×C7×C11 ⋊ C2×D13
HallC11×C13 ⋊ C2×D21
HallC7×C13 ⋊ C2×D3×C11
HallC7×C11 ⋊ D3×D13
HallC3×C13 ⋊ C2×C11×D7
HallC3×C11 ⋊ D7×D13
HallC3×C7 ⋊ C2×C11×D13
SylowC13 ⋊ C2×C11×D21
SylowC7 ⋊ D3×C11×D13
SylowC3 ⋊ C11×D7×D13

Subgroups

subgroupG/H
center, hypercenterC11D13×D21
commutator, cosocle, hypocenterC3×C7×C13C22×C11
FrattiniC1G
Fitting, socleC3×C7×C11×C13C22
LCSG ▷ C3×C7×C13
UCSC1 ◁ C11

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1056 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC11×D13×D63, C11×#10587717⋊D3, C11×#10587716⋊D3, …
maximal normal subgroup ofC11×#10587717⋊D3, C11×#10587716⋊D3, C11×D13×C3⋊AGL(1,𝔽7), …
maximal quotient ofC11×D13×D63, C3×C11×D13×D21, C11×D39⋊D21, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12012, 142);