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C2×#11745975 #14294458

order1920
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#11745975

Splittings

HallC3×C5 ⋊ C2×#339
SylowC5 ⋊ C2×#4555
SylowC3 ⋊ C2×#64752

Subgroups

subgroupG/H
centerC22×C4#1201
commutatorC3×C4×C5C2×C42
FrattiniC22×C4C2×D3×D5
FittingC23×C3×C4×C5C22
socleC23×C3×C5C22⋊C4
prime radicalC24×C3×C5D4
cosocleC22×C3×C4×C5C23
hypercenterC23×C4D3×D5
hypocenterC3×C5C2×#339
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C4 ◁ C23×C4

976 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, 20156);