Finite Group Databasebeta

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C2×C5×#5006 #14411918

order1920
automorphism?
homologyAbelianization (H1) = C23×C4×C5 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×C5×#5006

Splittings

FittingC2×C3×C5×#117 ⋊ C2
HallC3×C5 ⋊ C2×#410
SylowC3 ⋊ C2×C5×#410

Subgroups

subgroupG/H
centerC2×C4×C5(C2×D3)⋊C4
commutatorC22×C3C23×C4×C5
FrattiniC23C23×C5×D3
FittingC2×C3×C5×#117C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C5×#235C2
cosocleC23×C3C24×C5
hypercenterC2×C5×#117D3
hypocenterC3C2×C5×#410
LCSG ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4×C5 ◁ C23×C4×C5 ◁ C2×C5×#117

1576 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 137616);