Finite Group Databasebeta

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C3×C11×C22⋊(C61⋊C3) #37563559

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

Aliases

direct productC3×C11×C22⋊(C61⋊C3)
unambiguous semidirect product(C22×C3)⋊(C11×C61⋊C3)
unambiguous semidirect product(C22×C3×C11)⋊(C61⋊C3)
unambiguous semidirect product(C3×C61)⋊(C11×A4)
unambiguous semidirect product(C3×C11×C61)⋊A4

Splittings

Fitting, socleC22×C3×C11×C61 ⋊ C3
derived, HallC22×C61 ⋊ C32×C11
HallC22×C11×C61 ⋊ C32
HallC11×C61 ⋊ C3×A4
SylowC61 ⋊ C3×C11×A4
HallC22×C11 ⋊ C3×C61⋊C3
SylowC22 ⋊ C3×C11×C61⋊C3

Subgroups

subgroupG/H
center, hypercenterC3×C11C22⋊(C61⋊C3)
commutator, cosocle, hypocenterC22×C61C32×C11
FrattiniC1G
Fitting, socleC22×C3×C11×C61C3
LCSG ▷ C22×C61
UCSC1 ◁ C3×C11

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8052

Conjugacy classes & character table

2772 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24156, 117);