Finite Group Databasebeta

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C2×C5×D3×C22⋊C8 #14411588

order1920
automorphism?
homologyAbelianization (H1) = C23×C5×C8 · Schur multiplier (H2) = C27

Aliases

direct productC2×C5×D3×C22⋊C8

Splittings

FittingC2×C3×C5×C22⋊C8 ⋊ C2
HallC3×C5 ⋊ C22×C22⋊C8
SylowC3 ⋊ C22×C5×C22⋊C8

Subgroups

subgroupG/H
centerC22×C4×C5C22×D3
commutatorC2×C3C23×C5×C8
FrattiniC2×C4C23×C5×D3
FittingC2×C3×C5×C22⋊C8C2
socleC23×C3×C5C22×C4
prime radicalC24×C5×D3C4
cosocleC2×C3×C4C24×C5
hypercenterC2×C5×C22⋊C8D3
hypocenterC3C22×C5×C22⋊C8
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C4×C5 ◁ C2×C5×C22⋊C8

2144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 137286);