Finite Group Databasebeta

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C2×D5⋊#833 #14412050

order1920
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×D5⋊#833
unambiguous semidirect productD5⋊(C2×#833)

Splittings

HallC3×C5 ⋊ C22×#100
SylowC5 ⋊ C22×#833
SylowC3 ⋊ C2×D5⋊#100

Subgroups

subgroupG/H
centerC22C2×#6763
commutatorC22×C3×C5C23×C4
FrattiniC22C23×ΓL(1,𝔽16)
FittingC22×C3×C5×D4C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×D4×D5C2
cosocleC2×C3×Dic5C24
hypercenterC22×D4ΓL(1,𝔽16)
hypocenterC3×C5C22×#100
LCSG ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

1984 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

144 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 137748);