Finite Group Databasebeta

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C2×C3×D32×D5 #72217484

order2160
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C26

Aliases

direct productC2×C3×D32×D5

Splittings

Fitting, socleC2×C33×C5 ⋊ C23
derivedC32×C5 ⋊ C24×C3
HallC33×C5 ⋊ C24
SylowC33 ⋊ C23×D5
SylowC5 ⋊ C22×C3×D32

Subgroups

subgroupG/H
center, hypercenterC2×C3D32×D5
commutator, cosocle, hypocenterC32×C5C24×C3
FrattiniC1G
Fitting, socleC2×C33×C5C23
LCSG ▷ C32×C5
UCSC1 ◁ C2×C3

1284 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

216 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C3×D5×GO+(4,𝔽2), C2×C3×D32×AGL(1,𝔽5), C2×C3×D32⋊AGL(1,𝔽5), …
maximal normal subgroup ofC2×C3×D5×GO+(4,𝔽2), C2×C3×D32×AGL(1,𝔽5), C2×C3×D32⋊AGL(1,𝔽5), …
maximal quotient ofC2×C3×D5×((C3⋊D3)⋊C3)⋊C2, D32×D5×AGL(1,𝔽7), C3×D5×#3811

GAP

Past the SmallGroups library coverage — no SmallGroups id.