Finite Group Databasebeta

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C3×#10601269 #14297465

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

Aliases

direct productC3×#10601269

Splittings

FittingC2×C3×C5×C4⋊C8 ⋊ C2
HallC3×C5 ⋊ #1798
SylowC5 ⋊ C3×#1798

Subgroups

subgroupG/H
centerC22×C3×C4C22×D5
commutatorC23×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC2×C3×C5×C4⋊C8C2
socleC23×C3×C5C22×C4
prime radicalC23×C3×D5C2×C4
cosocleC22×C4×C5C23×C3
hypercenterC2×C3×C4⋊C8D5
hypocenterC5C3×#1798
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C22×C3×C4 ◁ C2×C3×C4⋊C8

624 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 23163);