Finite Group Databasebeta

C3×D4⋊#672 #14277753

order1920
automorphism?
homologyAbelianization (H1) = C2×C3×C16 · Schur multiplier (H2) = C22

Aliases

direct productC3×D4⋊#672
unambiguous semidirect productD4⋊(C3×#672)

Splittings

HallC3×C5 ⋊ D4⋊C16
SylowC5 ⋊ C3×D4⋊C16

Subgroups

subgroupG/H
centerC2×C3×C8C22⋊D5
commutatorC4×C5C2×C3×C16
FrattiniC4×C8C2×C3×D5
FittingC3×C5×C8×D4C2
socleC22×C3×C5C22⋊C8
prime radicalC2×C3×C5×D4C8
cosocleC4×C5×C8C22×C3
hypercenterC3×C8×D4D5
hypocenterC5C3×D4⋊C16
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C8 ◁ C3×C4×C8 ◁ C3×C8×D4

220 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 3451);