Finite Group Databasebeta

← Prev (#72219458) Next (#72219460) →

C3×C4×C5×AGL(1,𝔽9) #72219459

order4320
isoclinismisoclinic class of AGL(1,𝔽9)
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C8 · Schur multiplier (H2) = C4

Aliases

direct productC3×C4×C5×AGL(1,𝔽9)

Splittings

FittingC33×C4×C5 ⋊ C8
derivedC32 ⋊ C3×C4×C5×C8
HallC33×C5 ⋊ C4×C8
SylowC33 ⋊ C4×C5×C8

Subgroups

subgroupG/H
center, hypercenterC3×C4×C5AGL(1,𝔽9)
commutator, hypocenterC32C3×C4×C5×C8
FrattiniC2C2×C3×C5×AGL(1,𝔽9)
FittingC33×C4×C5C8
socleC2×C33×C5C2×C8
prime radicalC2×C3×C5×C3⋊D3C2×C4
cosocleC2×#157C22×C3×C5
LCSG ▷ C32
UCSC1 ◁ C3×C4×C5

220 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 100 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC3×C4×C5×AΓL(1,𝔽9)
maximal normal subgroup ofC3×C4×C5×AΓL(1,𝔽9)

GAP

Past the SmallGroups library coverage — no SmallGroups id.