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C3×#10601278 #14297682

order1920
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23

Aliases

direct productC3×#10601278

Splittings

HallC3×C5 ⋊ #1803
SylowC5 ⋊ C3×#1803

Subgroups

subgroupG/H
centerC23×C3C2×D20
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC2×C3×C5×C4⋊C8C2
socle, prime radicalC23×C3×C5C2×D4
cosocleC22×C4×C5C23×C3
hypercenterC2×C3×C4⋊C8D5
hypocenterC5C3×#1803
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C2×C3×C42 ◁ C2×C3×C4⋊C8

616 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1920

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 23380);