Finite Group Databasebeta

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C3×#10599894 #14314968

order1920
automorphism?
homologyAbelianization (H1) = C22×C3×C16 · Schur multiplier (H2) = C23

Aliases

direct productC3×#10599894

Splittings

FittingC3×C5×C22⋊C16 ⋊ C2
HallC3×C5 ⋊ D4×C16
SylowC5 ⋊ C3×D4×C16

Subgroups

subgroupG/H
centerC2×C3×C8C22×D5
commutatorC2×C5C22×C3×C16
FrattiniC2×C8C22×C3×D5
FittingC3×C5×C22⋊C16C2
socleC22×C3×C5C22×C8
prime radicalC2×C3×C22⋊D5C8
cosocleC2×C5×C8C23×C3
hypercenterC3×C22⋊C16D5
hypocenterC5C3×D4×C16
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C8 ◁ C3×C22⋊C16

348 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

480 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 40666);