Finite Group Databasebeta

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C3×C4×#3955 #14295420

order1920
automorphism?
homologyAbelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct productC3×C4×#3955

Splittings

FittingC3×C4×C5×M16 ⋊ C2
HallC3×C5 ⋊ C4×#100
SylowC5 ⋊ C3×C4×#100

Subgroups

subgroupG/H
centerC2×C3×C4#685
commutatorC22×C5C2×C3×C42
FrattiniC22×C4C22×C3×D5
FittingC3×C4×C5×M16C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×D20C22
cosocleC22×C4×C5C23×C3
hypercenterC3×C4×M16D5
hypocenterC5C3×C4×#100
LCSG ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C2×C3×C42 ◁ C3×C4×M16

720 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 21118);