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C5×AGL(2,𝔽3) #72213706

order2160
isoclinismisoclinic class of AGL(2,𝔽3)
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×AGL(2,𝔽3)

Splittings

Fitting, socleC32×C5 ⋊ GL(2,𝔽3)
derivedPSU(3,𝔽2)⋊C3 ⋊ C2×C5

Subgroups

subgroupG/H
center, hypercenterC5AGL(2,𝔽3)
commutator, cosocle, hypocenterPSU(3,𝔽2)⋊C3C2×C5
FrattiniC1G
Fitting, socleC32×C5GL(2,𝔽3)
LCSG ▷ PSU(3,𝔽2)⋊C3
UCSC1 ◁ C5

92 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

55 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD5×AGL(2,𝔽3), C3×C5×AGL(2,𝔽3), C2×C5×AGL(2,𝔽3), …
maximal normal subgroup ofD5×AGL(2,𝔽3), C3×C5×AGL(2,𝔽3), C2×C5×AGL(2,𝔽3)
maximal quotient ofC3×C5×AGL(2,𝔽3), C2×C5×AGL(2,𝔽3), C5×(PSU(3,𝔽2)⋊C3)⋊C4, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.