Finite Group Databasebeta

← Prev (#14296244) Next (#14296246) →

C8×C4⋊ΓL(1,𝔽16) #14296245

order1920
isoclinismisoclinic class of #6758
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct productC8×C4⋊ΓL(1,𝔽16)

Splittings

FittingC3×C4×C5×C8 ⋊ C4
HallC3×C5 ⋊ C8×C4⋊C4
SylowC5 ⋊ C8×C4⋊Dic3
SylowC3 ⋊ C8×C4⋊AGL(1,𝔽5)

Subgroups

subgroupG/H
centerC2×C8C2×ΓL(1,𝔽16)
commutatorC2×C3×C5C2×C4×C8
FrattiniC2×C4C22×ΓL(1,𝔽16)
FittingC3×C4×C5×C8C4
socleC22×C3×C5C2×C42
prime radicalC22×C3×D5C22×C4
cosocleC2×C3×C4×D5C23
hypercenterC4×C8ΓL(1,𝔽16)
hypocenterC3×C5C8×C4⋊C4
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C8 ◁ C4×C8

592 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 21943);