Finite Group Databasebeta

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C2×#11752459 #14319806

order1920
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×#11752459
unambiguous semidirect productD5⋊#5247

Splittings

FittingC25×C3×C5 ⋊ C4
HallC3×C5 ⋊ C2×#379
SylowC5 ⋊ C2×#5247
SylowC3 ⋊ C2×#65800

Subgroups

subgroupG/H
centerC23C22×ΓL(1,𝔽16)
commutatorC22×C3×C5C23×C4
FrattiniC22C23×ΓL(1,𝔽16)
FittingC25×C3×C5C4
socleC23×C3×C5C22×C4
prime radicalC25×C3×D5C2
cosocleC22×C3×D5C24
hypercenterC25ΓL(1,𝔽16)
hypocenterC3×C5C2×#379
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C25

6928 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

216 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 45504);