Finite Group Databasebeta

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C3×C5×C8×A4 #13087791

order1440
isoclinismisoclinic class of A4
automorphism?
homologyAbelianization (H1) = C32×C5×C8 · Schur multiplier (H2) = C2×C3

Aliases

direct productC3×C5×C8×A4
unambiguous semidirect product(C22×C8)⋊(C32×C5)
unambiguous semidirect product(C22×C3×C8)⋊(C3×C5)
unambiguous semidirect product(C22×C5×C8)⋊C32
unambiguous semidirect product(C22×C3×C5×C8)⋊C3

Splittings

FittingC22×C3×C5×C8 ⋊ C3
derivedC22 ⋊ C32×C5×C8
HallC22×C5×C8 ⋊ C32
SylowC22×C8 ⋊ C32×C5

Subgroups

subgroupG/H
center, hypercenterC3×C5×C8A4
commutator, hypocenterC22C32×C5×C8
FrattiniC4C2×C3×C5×A4
FittingC22×C3×C5×C8C3
socleC23×C3×C5C3×C4
prime radicalC2×C3×C5×A4C4
cosocleC22×C4C2×C32×C5
LCSG ▷ C22
UCSC1 ◁ C3×C5×C8

136 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 360

Conjugacy classes & character table

480 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 4108);