Finite Group Databasebeta

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C2×C3×D5×C4⋊C8 #14412962

order1920
automorphism?
homologyAbelianization (H1) = C23×C3×C8 · Schur multiplier (H2) = C26

Aliases

direct productC2×C3×D5×C4⋊C8

Splittings

FittingC2×C3×C5×C4⋊C8 ⋊ C2
HallC3×C5 ⋊ C22×C4⋊C8
SylowC5 ⋊ C22×C3×C4⋊C8

Subgroups

subgroupG/H
centerC22×C3×C4C22×D5
commutatorC2×C5C23×C3×C8
FrattiniC2×C4C23×C3×D5
FittingC2×C3×C5×C4⋊C8C2
socleC23×C3×C5C22×C4
prime radicalC23×C3×D5C2×C4
cosocleC2×C4×C5C24×C3
hypercenterC2×C3×C4⋊C8D5
hypocenterC5C22×C3×C4⋊C8
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3×C4 ◁ C2×C3×C4⋊C8

1280 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 138660);