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#95×ΓL(1,𝔽16) #14279845

order1920
automorphism?
homologyAbelianization (H1) = C43 · Schur multiplier (H2) = C23×C42

Aliases

direct product#95×ΓL(1,𝔽16)

Splittings

FittingC3×C5×#95 ⋊ C4
HallC3×C5 ⋊ C4×#95
SylowC5 ⋊ Dic3×#95
SylowC3 ⋊ AGL(1,𝔽5)×#95

Subgroups

subgroupG/H
center, FrattiniC23C22×ΓL(1,𝔽16)
commutatorC2×C3×C5C43
FittingC3×C5×#95C4
socleC23×C3×C5C22×C4
prime radical, cosocleC23×C3×D5C23
hypercenter#95ΓL(1,𝔽16)
hypocenterC3×C5C4×#95
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #95

1504 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 5543);