Finite Group Databasebeta

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C16×#1202 #14315002

order1920
isoclinismisoclinic class of #1201
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C23

Aliases

direct productC16×#1202

Splittings

HallC3×C5 ⋊ D4×C16
SylowC5 ⋊ C16×#67
SylowC3 ⋊ C16×D20

Subgroups

subgroupG/H
center, hypercenterC2×C16D3×D5
commutatorC2×C3×C5C22×C16
FrattiniC2×C8C2×D3×D5
FittingC2×C3×C5×C16C22
socleC22×C3×C5C22×C8
prime radicalC2×#1202C8
cosocleC2×C3×C5×C8C23
hypocenterC3×C5D4×C16
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C16

348 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 40700);