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C2×C3×D3×ΓL(1,𝔽16) #72217626

order2160
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×C3×D3×ΓL(1,𝔽16)

Splittings

Fitting, socleC2×C33×C5 ⋊ C2×C4
derivedC32×C5 ⋊ C22×C3×C4
HallC33×C5 ⋊ C22×C4
SylowC33 ⋊ C22×AGL(1,𝔽5)
SylowC5 ⋊ C2×C3×D3×Dic3

Subgroups

subgroupG/H
center, hypercenterC2×C3D3×ΓL(1,𝔽16)
commutator, hypocenterC32×C5C22×C3×C4
FrattiniC1G
Fitting, socleC2×C33×C5C2×C4
prime radicalC2×C32×D3×D5C2
cosocleC32×D5C23×C3
LCSG ▷ C32×C5
UCSC1 ◁ C2×C3

580 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

162 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C3×D32×AGL(1,𝔽5), C2×C3×((C3⋊D3)⋊C3)⋊AGL(1,𝔽5), C2×C3×#11761932, …
maximal normal subgroup ofC2×C3×D32×AGL(1,𝔽5), C2×D3×ΓL(1,𝔽16)⋊D3, C3×D3×Dic3×AGL(1,𝔽5), …
maximal quotient ofC2×C3×((C3⋊D3)⋊C3)⋊AGL(1,𝔽5), D3×AGL(1,𝔽7)×ΓL(1,𝔽16), C3×#67⋊ΓL(1,𝔽16)

GAP

Past the SmallGroups library coverage — no SmallGroups id.