Finite Group Databasebeta

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D3×C11×D61⋊C3 #37563508

order24156
automorphism?
homologyAbelianization (H1) = C22×C3×C11 · Schur multiplier (H2) = C2

Aliases

direct productD3×C11×D61⋊C3
unambiguous semidirect productD61⋊(C3×D3×C11)
unambiguous semidirect product(D3×D61)⋊(C3×C11)
unambiguous semidirect product(C3×D61⋊C3)⋊(C2×C11)
unambiguous semidirect product(D3×C61⋊C3)⋊(C2×C11)
unambiguous semidirect product(C3⋊(D61⋊C3))⋊(C2×C11)
unambiguous semidirect product(D3×C11×D61)⋊C3

Splittings

Fitting, socleC3×C11×C61 ⋊ C22×C3
derivedC3×C61 ⋊ C22×C3×C11
HallC3×C11×C61⋊C3 ⋊ C22
HallC11×C61 ⋊ C2×C3×D3
HallC3×C61⋊C3 ⋊ C22×C11
SylowC61 ⋊ C2×C3×D3×C11

Subgroups

subgroupG/H
center, hypercenterC11D3×D61⋊C3
commutator, cosocle, hypocenterC3×C61C22×C3×C11
FrattiniC1G
Fitting, socleC3×C11×C61C22×C3
LCSG ▷ C3×C61
UCSC1 ◁ C11

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2013

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24156, 66);