Finite Group Databasebeta

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C2×C3×C11×D61⋊C3 #37563516

order24156
automorphism?
homologyAbelianization (H1) = C22×C32×C11 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C3×C11×D61⋊C3
unambiguous semidirect productD61⋊(C2×C32×C11)
unambiguous semidirect product(C61⋊C3)⋊(C22×C3×C11)
unambiguous semidirect product(C2×D61)⋊(C32×C11)
unambiguous semidirect product(C2×C61⋊C3)⋊(C2×C3×C11)
unambiguous semidirect product(C2×C3×D61)⋊(C3×C11)
unambiguous semidirect product(C2×C11×D61)⋊C32
unambiguous semidirect product(C2×C3×C11×D61)⋊C3

Splittings

Fitting, socleC2×C3×C11×C61 ⋊ C2×C3
derived, SylowC61 ⋊ C22×C32×C11
HallC3×C11×C61⋊C3 ⋊ C22
HallC2×C11×D61 ⋊ C32
HallC11×C61 ⋊ C22×C32
HallC3×C61⋊C3 ⋊ C22×C11
HallC2×D61 ⋊ C32×C11

Subgroups

subgroupG/H
center, hypercenterC2×C3×C11D61⋊C3
commutator, cosocle, hypocenterC61C22×C32×C11
FrattiniC1G
Fitting, socleC2×C3×C11×C61C2×C3
LCSG ▷ C61
UCSC1 ◁ C2×C3×C11

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4026

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24156, 74);