Finite Group Databasebeta

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C2×C5×#4956 #14320275

order1920
automorphism?
homologyAbelianization (H1) = C23×C4×C5 · Schur multiplier (H2) = C28

Aliases

direct productC2×C5×#4956

Splittings

FittingC22×C3×C5×C22⋊C4 ⋊ C2
HallC3×C5 ⋊ C2×#386
SylowC3 ⋊ C2×C5×#386

Subgroups

subgroupG/H
centerC24×C5C22×D3
commutatorC22×C3C23×C4×C5
FrattiniC23C23×C5×D3
FittingC22×C3×C5×C22⋊C4C2
socleC24×C3×C5C23
prime radicalC23×C5×#67C2
cosocleC23×C3C24×C5
hypercenterC22×C5×C22⋊C4D3
hypocenterC3C2×C5×#386
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C24×C5 ◁ C22×C5×C22⋊C4

3152 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 45973);