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C32×C8×A4 #11723735

order864
isoclinismisoclinic class of A4
automorphism?
homologyAbelianization (H1) = C33×C8 · Schur multiplier (H2) = C2×C33

Aliases

direct productC32×C8×A4
unambiguous semidirect product(C22×C8)⋊C33
unambiguous semidirect product(C22×C3×C8)⋊C32

Splittings

FittingC22×C32×C8 ⋊ C3
derivedC22 ⋊ C33×C8
SylowC22×C8 ⋊ C33

Subgroups

subgroupG/H
center, hypercenterC32×C8A4
commutator, hypocenterC22C33×C8
FrattiniC4C2×C32×A4
FittingC22×C32×C8C3
socleC23×C32C3×C4
prime radicalC2×C32×A4C4
cosocleC22×C4C2×C33
LCSG ▷ C22
UCSC1 ◁ C32×C8

284 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 216

Conjugacy classes & character table

288 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC32×A4⋊C16, C3×C3⋊(A4⋊C16), C3⋊(C3⋊(A4⋊C16)), …
maximal normal subgroup ofC32×A4⋊C16, C3×C3⋊(A4⋊C16), C3⋊(C3⋊(A4⋊C16)), …
maximal quotient ofC32×C8×SL(2,𝔽3), C32×A4×C16, C32×#504⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(864, 3702);