Finite Group Databasebeta

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C3×D4×#685 #14325896

order1920
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C27

Aliases

direct productC3×D4×#685

Splittings

FittingC2×C3×C4×C5×D4 ⋊ C2
HallC3×C5 ⋊ D4×C22⋊C4
SylowC5 ⋊ C3×D4×C22⋊C4

Subgroups

subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC2×C3×C4×C5×D4C2
socleC23×C3×C5C24
prime radicalC22×C3×D4×D5C2
cosocleC23×C5C24×C3
hypercenterC2×C3×C4×D4D5
hypocenterC5C3×D4×C22⋊C4
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C2×C3×C4×D4

2504 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 51594);