Finite Group Databasebeta

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C22×C3×#3992 #14411199

order1920
isoclinismisoclinic class of #700
automorphism?
homologyAbelianization (H1) = C22×C3×C42 · Schur multiplier (H2) = C26

Aliases

direct productC22×C3×#3992

Splittings

FittingC22×C3×C5×C8 ⋊ C4
HallC3×C5 ⋊ C22×#97
SylowC5 ⋊ C22×C3×#97

Subgroups

subgroupG/H
centerC22×C3×C4C2×AGL(1,𝔽5)
commutatorC2×C5C22×C3×C42
FrattiniC4C23×C3×AGL(1,𝔽5)
FittingC22×C3×C5×C8C4
socleC23×C3×C5C42
prime radicalC23×C3×D5C2×C4
cosocleC4×D5C24×C3
hypercenterC22×C3×C8AGL(1,𝔽5)
hypocenterC5C22×C3×#97
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3×C4 ◁ C22×C3×C8

1360 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

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, 136897);