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C2×D5×GO+(4,𝔽2) #13089573

order1440
isoclinismisoclinic class of D5×GO+(4,𝔽2)
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×D5×GO+(4,𝔽2)
unambiguous semidirect product(D5×#157)⋊C22
unambiguous semidirect product(C5×GO+(4,𝔽2))⋊C22
unambiguous semidirect product(D32⋊D5)⋊C22
unambiguous semidirect product(#157⋊D5)⋊C22
unambiguous semidirect product(D32×D5)⋊C22

Splittings

Fitting, socleC2×C32×C5 ⋊ C2×D4
HallC32×C5 ⋊ C22×D4
SylowC32 ⋊ C2×D4×D5
SylowC5 ⋊ C22×GO+(4,𝔽2)

Subgroups

subgroupG/H
center, hypercenterC2D5×GO+(4,𝔽2)
commutator, cosocleC5×C3⋊D3C24
FrattiniC1G
Fitting, socleC2×C32×C5C2×D4
hypocenterC32×C5C22×D4
LCSG ▷ C5×C3⋊D3 ▷ C32×C5
UCSC1 ◁ C2

740 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 740 conjugacy classes of subgroups — too many to draw. Only its 104 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) = 60

Conjugacy classes & character table

72 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C3×D5×GO+(4,𝔽2), C2×AGL(1,𝔽5)×GO+(4,𝔽2), C2×D5×AΓL(1,𝔽9), …
maximal normal subgroup ofC2×C3×D5×GO+(4,𝔽2), C2×AGL(1,𝔽5)×GO+(4,𝔽2), C2×D5×AΓL(1,𝔽9), …
maximal quotient ofC2×C3×D5×GO+(4,𝔽2), D5×#13049813, D5×#64241

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 5890);