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C2×#11752377 #14411310

order1920
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#11752377

Splittings

FittingC22×C3×C5×C8 ⋊ C4
HallC3×C5 ⋊ C2×#405
SylowC5 ⋊ C2×#5101
SylowC3 ⋊ C2×#65718

Subgroups

subgroupG/H
centerC2×C8C2×ΓL(1,𝔽16)
commutatorC2×C3×C5C22×C42
FrattiniC4C23×ΓL(1,𝔽16)
FittingC22×C3×C5×C8C4
socleC22×C3×C5C2×C42
prime radicalC23×C3×D5C2×C4
cosocleC3×C4×D5C24
hypercenterC22×C8ΓL(1,𝔽16)
hypocenterC3×C5C2×#405
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C8 ◁ C22×C8

1184 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 137008);