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C2×#11751970 #14416464

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

Aliases

direct productC2×#11751970
unambiguous semidirect productD5⋊#4789

Splittings

HallC3×C5 ⋊ C2×#441
SylowC5 ⋊ C2×#4789
SylowC3 ⋊ C2×#65739

Subgroups

subgroupG/H
centerC22#67⋊AGL(1,𝔽5)
commutatorC3×C4×C5C23×C4
FrattiniC4C22×D3×AGL(1,𝔽5)
FittingC2×C3×C5×Q8C2×C4
socleC22×C3×C5C4×D4
prime radicalC22×C3×D5C2×D4
cosocleC3×C4×D5C24
hypercenterC2×Q8D3×AGL(1,𝔽5)
hypocenterC3×C5C2×#441
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q8

960 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

96 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 142162);