Finite Group Databasebeta

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C2×C3×#65018 #14414814

order1920
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×C3×#65018

Splittings

FittingC2×C3×C5×C22⋊C8 ⋊ C2
HallC3×C5 ⋊ C2×#436
SylowC5 ⋊ C2×C3×#436

Subgroups

subgroupG/H
centerC22×C3×C4C22×D5
commutatorC22×C5C23×C3×C4
FrattiniC2×C4C23×C3×D5
FittingC2×C3×C5×C22⋊C8C2
socleC23×C3×C5C22×C4
prime radicalC22×C3×C22⋊D5C4
cosocleC2×C4×C5C24×C3
hypercenterC2×C3×C22⋊C8D5
hypocenterC5C2×C3×#436
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3×C4 ◁ C2×C3×C22⋊C8

1104 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 140512);