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C4×C5×AGL(2,𝔽3) #72219453

order8640
isoclinismisoclinic class of AGL(2,𝔽3)
automorphism?
homologyAbelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C2

Aliases

direct productC4×C5×AGL(2,𝔽3)

Splittings

FittingC32×C4×C5 ⋊ GL(2,𝔽3)
derivedPSU(3,𝔽2)⋊C3 ⋊ C2×C4×C5

Subgroups

subgroupG/H
center, hypercenterC4×C5AGL(2,𝔽3)
commutator, hypocenterPSU(3,𝔽2)⋊C3C2×C4×C5
FrattiniC2C2×C5×AGL(2,𝔽3)
FittingC32×C4×C5GL(2,𝔽3)
socleC2×C32×C5C2×GL(2,𝔽3)
prime radicalC2×C5×AGL(2,𝔽3)C2
cosocleC2×PSU(3,𝔽2)⋊C3C22×C5
LCSG ▷ PSU(3,𝔽2)⋊C3
UCSC1 ◁ C4×C5

492 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 44 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

220 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C4×C5×AGL(2,𝔽3)
maximal normal subgroup ofC3×C4×C5×AGL(2,𝔽3)
maximal quotient ofC3×C4×C5×AGL(2,𝔽3)

GAP

Past the SmallGroups library coverage — no SmallGroups id.