Finite Group Databasebeta

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C22×C3×#3965 #14412045

order1920
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C26

Aliases

direct productC22×C3×#3965

Splittings

HallC3×C5 ⋊ C22×#100
SylowC5 ⋊ C22×C3×#100

Subgroups

subgroupG/H
centerC23×C3C22⋊Dic5
commutatorC22×C5C23×C3×C4
FrattiniC2×C4C23×C3×D5
Fitting, prime radicalC23×C3×C5×D4C2
socleC23×C3×C5C22⋊C4
cosocleC2×C4×C5C24×C3
hypercenterC23×C3×D4D5
hypocenterC5C22×C3×#100
LCSG ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C23×C3×C4 ◁ C23×C3×D4

1984 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

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, 137743);