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C23×C3×C22⋊AGL(1,𝔽5) #14478686

order1920
isoclinismisoclinic class of #700
automorphism?
homologyAbelianization (H1) = C24×C3×C4 · Schur multiplier (H2) = C211

Aliases

direct productC23×C3×C22⋊AGL(1,𝔽5)
unambiguous semidirect productD5⋊(C22×C3×C22⋊C4)
unambiguous semidirect product(C2×AGL(1,𝔽5))⋊(C24×C3)

Splittings

FittingC25×C3×C5 ⋊ C4
HallC3×C5 ⋊ C23×C22⋊C4
SylowC5 ⋊ C23×C3×C22⋊C4

Subgroups

subgroupG/H
centerC24×C3C2×AGL(1,𝔽5)
commutatorC2×C5C24×C3×C4
FrattiniC2C24×C3×AGL(1,𝔽5)
FittingC25×C3×C5C4
socleC24×C3×C5C2×C4
prime radicalC25×C3×D5C2
cosocleC2×D5C25×C3
hypercenterC25×C3AGL(1,𝔽5)
hypocenterC5C23×C3×C22⋊C4
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C24×C3 ◁ C25×C3

9264 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 204384);