Finite Group Databasebeta

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C3×(C2×AGL(1,𝔽5))⋊C16 #14278684

order1920
automorphism?
homologyAbelianization (H1) = C3×C4×C16 · Schur multiplier (H2) = C23

Aliases

direct productC3×(C2×AGL(1,𝔽5))⋊C16
unambiguous semidirect product(C2×AGL(1,𝔽5))⋊(C3×C16)

Splittings

FittingC2×C3×C5×C16 ⋊ C4
HallC3×C5 ⋊ #1374
SylowC5 ⋊ C3×#1374

Subgroups

subgroupG/H
centerC2×C3×C8C2×AGL(1,𝔽5)
commutatorC2×C5C3×C4×C16
FrattiniC2×C8C2×C3×AGL(1,𝔽5)
FittingC2×C3×C5×C16C4
socleC22×C3×C5C4×C8
prime radicalC22×C3×D5C2×C8
cosocleC2×C8×D5C22×C3
hypercenterC2×C3×C16AGL(1,𝔽5)
hypocenterC5C3×#1374
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C8 ◁ C2×C3×C16

320 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

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, 4382);