Finite Group Databasebeta

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C3×C4×#3990 #14312593

order1920
isoclinismisoclinic class of #700
automorphism?
homologyAbelianization (H1) = C2×C3×C4×C8 · Schur multiplier (H2) = C2×C4

Aliases

direct productC3×C4×#3990

Splittings

HallC3×C5 ⋊ C4×M32
SylowC5 ⋊ C3×C4×M32

Subgroups

subgroupG/H
centerC3×C42C2×AGL(1,𝔽5)
commutatorC2×C5C2×C3×C4×C8
FrattiniC2×C4C22×C3×AGL(1,𝔽5)
FittingC3×C4×C5×C8C4
socleC22×C3×C5C22×C8
prime radicalC22×C3×D5C2×C8
cosocleC2×#168C23×C3
hypercenterC3×C4×C8AGL(1,𝔽5)
hypocenterC5C3×C4×M32
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C3×C42 ◁ C3×C4×C8

392 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, 38291);