Finite Group Databasebeta

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C2×C4×#6758 #14411243

order1920
isoclinismisoclinic class of #6758
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×C4×#6758

Splittings

HallC3×C5 ⋊ C2×C4×M16
SylowC5 ⋊ C2×C4×#208
SylowC3 ⋊ C2×C4×#700

Subgroups

subgroupG/H
centerC22×C4C2×ΓL(1,𝔽16)
commutatorC2×C3×C5C22×C42
FrattiniC22C23×ΓL(1,𝔽16)
FittingC2×C3×C42×C5C4
socleC23×C3×C5C22×C4
prime radicalC23×C3×D5C2×C4
cosocleC2×C3×Dic5C24
hypercenterC2×C42ΓL(1,𝔽16)
hypocenterC3×C5C2×C4×M16
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C4 ◁ C2×C42

1312 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

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, 136941);