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C3×#10624306 #72217328

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

Aliases

direct productC3×#10624306

Splittings

Fitting, socle, HallC33×C5 ⋊ C4⋊C4
SylowC33 ⋊ C4⋊AGL(1,𝔽5)
SylowC5 ⋊ C3×#3773

Subgroups

subgroupG/H
center, hypercenterC3#10624306
commutatorC5×C3⋊D3C2×C3×C4
FrattiniC1G
Fitting, socleC33×C5C4⋊C4
prime radicalC3×D5×C3⋊D3C22
cosocleD5×C3⋊D3C22×C3
hypocenterC32×C5C3×C4⋊C4
LCSG ▷ C5×C3⋊D3 ▷ C32×C5
UCSC1 ◁ C3

192 conjugacy classes of subgroups; only the 34 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 34 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

72 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×AGL(1,𝔽5)×GO+(4,𝔽2), C3×PSU(3,𝔽2)⋊AGL(1,𝔽5), C3×AGL(1,𝔽9)⋊AGL(1,𝔽5), …
maximal normal subgroup ofC3×AGL(1,𝔽5)×GO+(4,𝔽2), C3×PSU(3,𝔽2)⋊AGL(1,𝔽5), C3×AGL(1,𝔽9)⋊AGL(1,𝔽5), …
maximal quotient ofC2×C3×#10624306

GAP

Past the SmallGroups library coverage — no SmallGroups id.