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C2×C32×D4×D5 #13089447

order1440
automorphism?
homologyAbelianization (H1) = C24×C32 · Schur multiplier (H2) = C26×C3

Aliases

direct productC2×C32×D4×D5

Splittings

FittingC2×C32×C5×D4 ⋊ C2
HallC32×C5 ⋊ C22×D4
SylowC5 ⋊ C22×C32×D4

Subgroups

subgroupG/H
centerC22×C32C22×D5
commutator, cosocleC2×C5C24×C32
FrattiniC2C23×C32×D5
FittingC2×C32×C5×D4C2
socleC22×C32×C5C23
hypercenterC2×C32×D4D5
hypocenterC5C22×C32×D4
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C32 ◁ C2×C32×D4

1416 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 360

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC2×D4×D5×C3⋊D3, C2×C32×D4×AGL(1,𝔽5), C2×D4×C3⋊ΓL(1,𝔽16), …
maximal normal subgroup ofC2×D4×D5×C3⋊D3, C2×C32×D4×AGL(1,𝔽5), C2×D4×C3⋊ΓL(1,𝔽16), …
maximal quotient ofC32×D5×#120, C2×C32×D4×C5⋊D5, C2×C32×#87886, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 5764);