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C3×#10604273 #14282121

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

Aliases

direct productC3×#10604273

Splittings

HallC3×C5 ⋊ #1487
SylowC5 ⋊ C3×#1487

Subgroups

subgroupG/H
centerC22×C3C2×C22⋊AGL(1,𝔽5)
commutatorC2×C4×C5C22×C3×C4
FrattiniC2×C4C22×C3×AGL(1,𝔽5)
FittingC2×C3×C5×C4⋊C4C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C3×C5C22⋊C4
cosocleC4×Dic5C23×C3
hypercenterC2×C3×C4⋊C4AGL(1,𝔽5)
hypocenterC5C3×#1487
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C2×C3×C4⋊C4

496 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

174 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 7819);