Finite Group Databasebeta

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C4×C5×#67⋊C4 #14319552

order1920
automorphism?
homologyAbelianization (H1) = C22×C42×C5 · Schur multiplier (H2) = C25×C4

Aliases

direct productC4×C5×#67⋊C4

Splittings

FittingC3×C4×C5×C22⋊C4 ⋊ C2
HallC3×C5 ⋊ C42×D4
SylowC3 ⋊ C42×C5×D4

Subgroups

subgroupG/H
centerC22×C4×C5C22×D3
commutatorC2×C3C22×C42×C5
FrattiniC23C23×C5×D3
FittingC3×C4×C5×C22⋊C4C2
socleC23×C3×C5C24
prime radicalC22×C5×#67C22
cosocleC23×C3C24×C5
hypercenterC4×C5×C22⋊C4D3
hypocenterC3C42×C5×D4
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C4×C5 ◁ C4×C5×C22⋊C4

1848 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

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, 45250);