Finite Group Databasebeta

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C2×C5×#4463 #14314402

order1920
isoclinismisoclinic class of #204
automorphism?
homologyAbelianization (H1) = C22×C5×C8 · Schur multiplier (H2) = C22

Aliases

direct productC2×C5×#4463

Splittings

HallC3×C5 ⋊ C2×#364
SylowC3 ⋊ C2×C5×#364

Subgroups

subgroupG/H
centerC2×C5×C8D12
commutatorC3×C4C22×C5×C8
FrattiniC2×C8C22×C5×D3
FittingC2×C3×C4×C5×C8C2
socleC22×C3×C5C4⋊C8
prime radicalC23×C3×C5M16
cosocleC2×C3×C8C23×C5
hypercenterC2×C4×C5×C8D3
hypocenterC3C2×C5×#364
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C5×C8 ◁ C22×C5×C8 ◁ C2×C4×C5×C8

336 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

600 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 40100);