Finite Group Databasebeta

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C2×C3×D5×(C3⋊D3)⋊C3 #72217529

order3240
automorphism?
homologyAbelianization (H1) = C23×C32 · Schur multiplier (H2) = C23×C32

Aliases

direct productC2×C3×D5×(C3⋊D3)⋊C3

Splittings

FittingC2×C3×C5×H(3,𝔽3) ⋊ C22
derivedC32×C5 ⋊ C23×C32
HallC3×C5×H(3,𝔽3) ⋊ C23
SylowC3×H(3,𝔽3) ⋊ C22×D5
SylowC5 ⋊ C22×C3×(C3⋊D3)⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C3D5×(C3⋊D3)⋊C3
commutator, cosocle, hypocenterC32×C5C23×C32
FrattiniC3C2×C32×D3×D5
FittingC2×C3×C5×H(3,𝔽3)C22
socleC2×C32×C5C2×C3×D3
LCSG ▷ C32×C5
UCSC1 ◁ C2×C3

820 conjugacy classes of subgroups; only the 182 normal subgroups are shown.

normal subgroups only

This group has 820 conjugacy classes of subgroups — too many to draw. Only its 182 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

240 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C3×D5×PSU(3,𝔽2)⋊C3, C2×C3×AGL(1,𝔽5)×(C3⋊D3)⋊C3, C2×C3×D5×((C3⋊D3)⋊C3)⋊C2, …
maximal normal subgroup ofC2×C3×AGL(1,𝔽5)×(C3⋊D3)⋊C3, C2×C3×D5×((C3⋊D3)⋊C3)⋊C2, C2×C3×((C3⋊D3)⋊C3)⋊AGL(1,𝔽5)

GAP

Past the SmallGroups library coverage — no SmallGroups id.