Finite Group Databasebeta

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C3×#10602410 #14297560

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

Aliases

direct productC3×#10602410

Splittings

HallC3×C5 ⋊ #1800
SylowC5 ⋊ C3×#1800

Subgroups

subgroupG/H
centerC22×C3C2×C22⋊Dic5
commutatorC23×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC2×C3×C4×C5×D4C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×C5×D4C22
cosocleC22×C4×C5C23×C3
hypercenterC2×C3×C4×D4D5
hypocenterC5C3×#1800
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C2×C3×C42 ◁ C2×C3×C4×D4

672 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 23258);