Finite Group Databasebeta

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C2×#11747468 #14416500

order1920
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#11747468

Splittings

HallC3×C5 ⋊ C2×#442
SylowC5 ⋊ C2×#5014
SylowC3 ⋊ C2×#65074

Subgroups

subgroupG/H
centerC23D5×#67
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C2×D4
prime radicalC22×#6652C2
cosocleC2×C3×C4×C5C24
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5C2×#442
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

1216 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, 142198);