Finite Group Databasebeta

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C2×C4×C5×PSU(3,𝔽2)⋊C3 #72219475

order8640
isoclinismisoclinic class of PSU(3,𝔽2)⋊C3
automorphism?
homologyAbelianization (H1) = C2×C3×C4×C5 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C4×C5×PSU(3,𝔽2)⋊C3

Splittings

FittingC2×C32×C4×C5 ⋊ SL(2,𝔽3)
derivedPSU(3,𝔽2) ⋊ C2×C3×C4×C5

Subgroups

subgroupG/H
center, hypercenterC2×C4×C5PSU(3,𝔽2)⋊C3
commutator, hypocenterPSU(3,𝔽2)C2×C3×C4×C5
FrattiniC2C22×C5×PSU(3,𝔽2)⋊C3
FittingC2×C32×C4×C5SL(2,𝔽3)
socleC22×C32×C5C2×SL(2,𝔽3)
prime radicalC22×C5×PSU(3,𝔽2)⋊C3C2
cosocleC2×PSU(3,𝔽2)C22×C3×C5
LCSG ▷ PSU(3,𝔽2)
UCSC1 ◁ C2×C4×C5

572 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 102 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

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

GAP

Past the SmallGroups library coverage — no SmallGroups id.