Finite Group Databasebeta

← Prev (#14319439) Next (#14319441) →

C2×C3×C4×C4⋊AGL(1,𝔽5) #14319440

order1920
isoclinismisoclinic class of #700
automorphism?
homologyAbelianization (H1) = C22×C3×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×C3×C4×C4⋊AGL(1,𝔽5)

Splittings

FittingC2×C3×C42×C5 ⋊ C4
HallC3×C5 ⋊ C2×C4×C4⋊C4
SylowC5 ⋊ C2×C3×C4×C4⋊C4

Subgroups

subgroupG/H
centerC22×C3×C4C2×AGL(1,𝔽5)
commutatorC2×C5C22×C3×C42
FrattiniC22C23×C3×AGL(1,𝔽5)
FittingC2×C3×C42×C5C4
socleC23×C3×C5C22×C4
prime radicalC23×C3×D5C23
cosocleC22×D5C24×C3
hypercenterC2×C3×C42AGL(1,𝔽5)
hypocenterC5C2×C3×C4×C4⋊C4
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3×C4 ◁ C2×C3×C42

1856 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, 45138);