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C3×#10598793 #14276886

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

Aliases

direct productC3×#10598793

Splittings

HallC3×C5 ⋊ #1283
SylowC5 ⋊ C3×#1283

Subgroups

subgroupG/H
centerC22×C3(C2×AGL(1,𝔽5))⋊C4
commutatorC22×C5C3×C4×C8
FrattiniC22×C4C2×C3×AGL(1,𝔽5)
FittingC2×C3×C5×M16C4
socleC22×C3×C5#95
prime radicalC23×C3×C5C42
cosocleC2×C4×Dic5C22×C3
hypercenterC2×C3×M16AGL(1,𝔽5)
hypocenterC5C3×#1283
LCSG ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C2×C3×M16

320 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 2584);