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C3×#10598796 #14278798

order1920
automorphism?
homologyAbelianization (H1) = C3×C4×C8 · Schur multiplier (H2) = C22

Aliases

direct productC3×#10598796

Splittings

HallC3×C5 ⋊ #1379
SylowC5 ⋊ C3×#1379

Subgroups

subgroupG/H
centerC2×C3×C4C22⋊AGL(1,𝔽5)
commutatorC4×C5C3×C4×C8
FrattiniC22×C4C2×C3×AGL(1,𝔽5)
FittingC2×C3×C5×M16C4
socleC22×C3×C5C22⋊C8
prime radicalC23×C3×C5M16
cosocleC22×#168C22×C3
hypercenterC2×C3×M16AGL(1,𝔽5)
hypocenterC5C3×#1379
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C22×C3×C4 ◁ C2×C3×M16

272 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

228 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 4496);