Finite Group Databasebeta

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C22×C3×C4⋊#168 #14412968

order1920
isoclinismisoclinic class of Dic10
automorphism?
homologyAbelianization (H1) = C23×C3×C8 · Schur multiplier (H2) = C26

Aliases

direct productC22×C3×C4⋊#168

Splittings

HallC3×C5 ⋊ C22×C4⋊C8
SylowC5 ⋊ C22×C3×C4⋊C8

Subgroups

subgroupG/H
centerC23×C3×C4C2×D5
commutatorC2×C5C23×C3×C8
FrattiniC2×C4C23×C3×D5
FittingC22×C3×C42×C5C2
socle, prime radicalC24×C3×C5C2×C4
cosocleC2×C4×C5C24×C3
hypercenterC22×C3×C42D5
hypocenterC5C22×C3×C4⋊C8
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C23×C3×C4 ◁ C22×C3×C42

1280 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1920

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 138666);