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C2×#11749173 #14411946

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

Aliases

direct productC2×#11749173

Splittings

HallC3×C5 ⋊ C2×#410
SylowC5 ⋊ C2×#4740
SylowC3 ⋊ C2×#65529

Subgroups

subgroupG/H
centerC22D3×C22⋊Dic5
commutatorC22×C3×C5C23×C4
FrattiniC23C22×D3×D5
FittingC22×C3×C5×D4C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C5×#237C2
cosocleC23×C3×C5C24
hypercenterC22×D4D3×D5
hypocenterC3×C5C2×#410
LCSG ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C24 ◁ C22×D4

1576 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

186 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 137644);