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C3×A4×C71 #14579394

order2556
isoclinismisoclinic class of A4
automorphism?
homologyAbelianization (H1) = C32×C71 · Schur multiplier (H2) = C2×C3

Aliases

direct productC3×A4×C71
unambiguous semidirect productC22⋊(C32×C71)
unambiguous semidirect product(C22×C3)⋊(C3×C71)
unambiguous semidirect product(C22×C71)⋊C32
unambiguous semidirect product(C22×C3×C71)⋊C3

Splittings

Fitting, socleC22×C3×C71 ⋊ C3
derived, SylowC22 ⋊ C32×C71
HallC22×C71 ⋊ C32

Subgroups

subgroupG/H
center, hypercenterC3×C71A4
commutator, cosocle, hypocenterC22C32×C71
FrattiniC1G
Fitting, socleC22×C3×C71C3
LCSG ▷ C22
UCSC1 ◁ C3×C71

28 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 852

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC3×A4×C71⋊C5, C3×C5×A4×C71, C3×A5×C71, …
maximal normal subgroup ofC3×A4×C71⋊C5, C3×C5×A4×C71, C3×A4×C71⋊C7, …
maximal quotient ofC3×C5×A4×C71, A4×ΓL(1,𝔽8)×C71, C3×C71×C22⋊ΓL(1,𝔽8), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2556, 25);