Finite Group Databasebeta

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C5×C22⋊C4×#67 #14325901

order1920
automorphism?
homologyAbelianization (H1) = C23×C4×C5 · Schur multiplier (H2) = C27

Aliases

direct productC5×C22⋊C4×#67

Splittings

FittingC22×C3×C5×C22⋊C4 ⋊ C2
HallC3×C5 ⋊ D4×C22⋊C4
SylowC3 ⋊ C5×D4×C22⋊C4

Subgroups

subgroupG/H
centerC23×C5C23×D3
commutatorC22×C3C23×C4×C5
FrattiniC23C23×C5×D3
FittingC22×C3×C5×C22⋊C4C2
socleC23×C3×C5C24
prime radicalC23×C5×#67C2
cosocleC23×C3C24×C5
hypercenterC22×C5×C22⋊C4D3
hypocenterC3C5×D4×C22⋊C4
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C5 ◁ C22×C5×C22⋊C4

2504 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 51599);