Finite Group Databasebeta

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C2×C5×#4964 #14413340

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

Aliases

direct productC2×C5×#4964

Splittings

HallC3×C5 ⋊ C2×#428
SylowC3 ⋊ C2×C5×#428

Subgroups

subgroupG/H
centerC23×C5C2×#67
commutatorC3×C4C23×C4×C5
FrattiniC2×C4C23×C5×D3
FittingC22×C3×C5×C4⋊C4C2
socleC23×C3×C5C2×D4
prime radicalC24×C3×C5D4
cosocleC2×C3×C4C24×C5
hypercenterC22×C5×C4⋊C4D3
hypocenterC3C2×C5×#428
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C5 ◁ C23×C4×C5 ◁ C22×C5×C4⋊C4

1072 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

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, 139038);