Finite Group Databasebeta

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C4×C5×D3×C16 #14312503

order1920
isoclinismisoclinic class of D3
automorphism?
homologyAbelianization (H1) = C2×C4×C5×C16 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4×C5×D3×C16

Splittings

FittingC3×C4×C5×C16 ⋊ C2
derived, SylowC3 ⋊ C2×C4×C5×C16
HallC3×C5 ⋊ C2×C4×C16

Subgroups

subgroupG/H
center, hypercenterC4×C5×C16D3
commutator, hypocenterC3C2×C4×C5×C16
FrattiniC2×C8C22×C5×D3
FittingC3×C4×C5×C16C2
socleC22×C3×C5C22×C8
prime radicalC22×C5×D3C2×C8
cosocleC2×C3×C8C23×C5
LCSG ▷ C3
UCSC1 ◁ C4×C5×C16

432 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 38201);