Finite Group Databasebeta

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C32×(C2×D3)⋊AGL(1,𝔽5) #72269739

order2160
automorphism?
homologyAbelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C22×C3

Aliases

direct productC32×(C2×D3)⋊AGL(1,𝔽5)

Splittings

HallC33×C5 ⋊ C22⋊C4
SylowC33 ⋊ C22⋊AGL(1,𝔽5)
SylowC5 ⋊ C32×(C2×D3)⋊C4

Subgroups

subgroupG/H
center, hypercenterC2×C32D3×AGL(1,𝔽5)
commutatorC2×C3×C5C2×C32×C4
FrattiniC2C32×D3×AGL(1,𝔽5)
Fitting, socleC2×C33×C5C2×C4
prime radicalC2×C32×D3×D5C2
cosocleC2×C3×D5C22×C32
hypocenterC3×C5C32×C22⋊C4
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C32

536 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 132 normal subgroups are shown.

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

Full subgroup data →

Presentation

transitive degreeμt(G) = 180

Conjugacy classes & character table

216 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×#13088405, C32×AGL(1,𝔽5)×#67, C3×#13088417
maximal normal subgroup ofC3×#13088405, C32×AGL(1,𝔽5)×#67, C3×#13088417

GAP

Past the SmallGroups library coverage — no SmallGroups id.