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C2×#11752360 #14411314

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

Aliases

direct productC2×#11752360

Splittings

HallC3×C5 ⋊ C2×#405
SylowC5 ⋊ C2×#4997
SylowC3 ⋊ C2×#65701

Subgroups

subgroupG/H
centerC23C22×ΓL(1,𝔽16)
commutatorC2×C3×C5C22×C42
FrattiniC22C23×ΓL(1,𝔽16)
FittingC2×C3×C5×C4⋊C4C4
socleC23×C3×C5C22×C4
prime radicalC23×C3×D5C2×C4
cosocleC2×C3×Dic5C24
hypercenterC2×C4⋊C4ΓL(1,𝔽16)
hypocenterC3×C5C2×#405
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4⋊C4

1184 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 137012);