Finite Group Databasebeta

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C3×C4×D5×Q16 #14416137

order1920
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C25

Aliases

direct productC3×C4×D5×Q16

Splittings

FittingC3×C4×C5×Q16 ⋊ C2
HallC3×C5 ⋊ C2×C4×Q16
SylowC5 ⋊ C2×C3×C4×Q16

Subgroups

subgroupG/H
centerC2×C3×C4D4×D5
commutatorC4×C5C23×C3×C4
FrattiniC2×C4C23×C3×D5
FittingC3×C4×C5×Q16C2
socleC22×C3×C5C22×D4
prime radicalC22×C3×D5C2×D4
cosocleC2×C4×C5C24×C3
hypercenterC3×C4×Q16D5
hypocenterC5C2×C3×C4×Q16
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C3×C42 ◁ C3×C4×Q16

976 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, 141835);