Finite Group Databasebeta

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C2×C3×C4⋊#674 #14314300

order1920
isoclinismisoclinic class of #700
automorphism?
homologyAbelianization (H1) = C22×C3×C16 · Schur multiplier (H2) = C23

Aliases

direct productC2×C3×C4⋊#674

Splittings

HallC3×C5 ⋊ C2×C4⋊C16
SylowC5 ⋊ C2×C3×C4⋊C16

Subgroups

subgroupG/H
centerC22×C3×C4C2×AGL(1,𝔽5)
commutatorC2×C5C22×C3×C16
FrattiniC2×C4C22×C3×AGL(1,𝔽5)
FittingC2×C3×C42×C5C4
socle, prime radicalC23×C3×C5C2×C8
cosocleC2×#168C23×C3
hypercenterC2×C3×C42AGL(1,𝔽5)
hypocenterC5C2×C3×C4⋊C16
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3×C4 ◁ C2×C3×C42

368 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1920

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 39998);