Finite Group Databasebeta

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C22×#91221 #14411200

order1920
isoclinismisoclinic class of #6758
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26

Aliases

direct productC22×#91221

Splittings

FittingC22×C3×C5×C8 ⋊ C4
HallC3×C5 ⋊ C22×#97
SylowC5 ⋊ C22×#815
SylowC3 ⋊ C22×#3992

Subgroups

subgroupG/H
centerC22×C4C2×ΓL(1,𝔽16)
commutatorC2×C3×C5C22×C42
FrattiniC4C23×ΓL(1,𝔽16)
FittingC22×C3×C5×C8C4
socleC23×C3×C5C42
prime radicalC23×C3×D5C2×C4
cosocleC3×C4×D5C24
hypercenterC22×C8ΓL(1,𝔽16)
hypocenterC3×C5C22×#97
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C4 ◁ C22×C8

1360 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 136898);