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C3×#10598771 #14276752

order1920
automorphism?
homologyAbelianization (H1) = C3×C4×C8 · Schur multiplier (H2) = C23

Aliases

direct productC3×#10598771

Splittings

HallC3×C5 ⋊ #1277
SylowC5 ⋊ C3×#1277

Subgroups

subgroupG/H
centerC23×C3C4⋊AGL(1,𝔽5)
commutatorC4×C5C3×C4×C8
FrattiniC22×C4C2×C3×AGL(1,𝔽5)
FittingC22×C3×C5×C8C4
socle, prime radicalC23×C3×C5C4⋊C4
cosocleC2×C4×Dic5C22×C3
hypercenterC22×C3×C8AGL(1,𝔽5)
hypocenterC5C3×#1277
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C22×C3×C4 ◁ C22×C3×C8

360 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1920

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 2450);