Finite Group Databasebeta

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C3×C4×C5×AGL(2,𝔽3) #72219472

order25920
isoclinismisoclinic class of AGL(2,𝔽3)
automorphism?
homologyAbelianization (H1) = C2×C3×C4×C5 · Schur multiplier (H2) = C2

Aliases

direct productC3×C4×C5×AGL(2,𝔽3)

Splittings

FittingC33×C4×C5 ⋊ GL(2,𝔽3)
derivedPSU(3,𝔽2)⋊C3 ⋊ C2×C3×C4×C5

Subgroups

subgroupG/H
center, hypercenterC3×C4×C5AGL(2,𝔽3)
commutator, hypocenterPSU(3,𝔽2)⋊C3C2×C3×C4×C5
FrattiniC2C2×C3×C5×AGL(2,𝔽3)
FittingC33×C4×C5GL(2,𝔽3)
socleC2×C33×C5C2×GL(2,𝔽3)
prime radicalC2×C3×C5×AGL(2,𝔽3)C2
cosocleC2×PSU(3,𝔽2)⋊C3C22×C3×C5
LCSG ▷ PSU(3,𝔽2)⋊C3
UCSC1 ◁ C3×C4×C5

1158 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 1158 conjugacy classes of subgroups — too many to draw. Only its 88 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

660 conjugacy classes. The character table is too large to display.

GAP

Past the SmallGroups library coverage — no SmallGroups id.