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C22⋊D5×#217 #14325941

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

Aliases

direct productC22⋊D5×#217

Splittings

HallC3×C5 ⋊ D4×C22⋊C4
SylowC5 ⋊ D4×#217
SylowC3 ⋊ C22⋊C4×C22⋊D5

Subgroups

subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC25×C3×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC23×C3×C22⋊D5C2
hypercenterC25D3×D5
hypocenterC3×C5D4×C22⋊C4
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C25

2504 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

234 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 51639);