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C3×AGL(1,𝔽5)×#95 #14279844

order1920
automorphism?
homologyAbelianization (H1) = C3×C43 · Schur multiplier (H2) = C23×C42

Aliases

direct productC3×AGL(1,𝔽5)×#95

Splittings

FittingC3×C5×#95 ⋊ C4
HallC3×C5 ⋊ C4×#95
SylowC5 ⋊ C3×C4×#95

Subgroups

subgroupG/H
centerC23×C3C22×AGL(1,𝔽5)
commutatorC2×C5C3×C43
FrattiniC23C22×C3×AGL(1,𝔽5)
FittingC3×C5×#95C4
socleC23×C3×C5C22×C4
prime radicalC23×C3×D5C23
cosocleC23×D5C23×C3
hypercenterC3×#95AGL(1,𝔽5)
hypocenterC5C3×C4×#95
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C3×#95

1504 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 5542);