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C3×A4×C41 #13093294

order1476
isoclinismisoclinic class of A4
automorphism?
homologyAbelianization (H1) = C32×C41 · Schur multiplier (H2) = C2×C3

Aliases

direct productC3×A4×C41
unambiguous semidirect productC22⋊(C32×C41)
unambiguous semidirect product(C22×C3)⋊(C3×C41)
unambiguous semidirect product(C22×C41)⋊C32
unambiguous semidirect product(C22×C3×C41)⋊C3

Splittings

Fitting, socleC22×C3×C41 ⋊ C3
derived, SylowC22 ⋊ C32×C41
HallC22×C41 ⋊ C32

Subgroups

subgroupG/H
center, hypercenterC3×C41A4
commutator, cosocle, hypocenterC22C32×C41
FrattiniC1G
Fitting, socleC22×C3×C41C3
LCSG ▷ C22
UCSC1 ◁ C3×C41

28 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 492

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC3×C11×A4×C41, A4×C13⋊C3×C41, C3×C41×C22⋊(C13⋊C3), …
maximal normal subgroup ofC3×C11×A4×C41, C3×A4×C13×C41, C3×A4×C17×C41, …
maximal quotient ofC3×C11×A4×C41, A4×C13⋊C3×C41, C3×C41×C22⋊(C13⋊C3), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1476, 30);