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C22×C3×GL(3,𝔽2) #72218673

order2016
isoclinismisoclinic class of GL(3,𝔽2)
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C22

Aliases

direct productC22×C3×GL(3,𝔽2)

Subgroups

subgroupG/H
center, Fitting, hypercenterC22×C3GL(3,𝔽2)
commutator, hypocenterGL(3,𝔽2)C22×C3
FrattiniC1G
LCSG ▷ GL(3,𝔽2)
UCSC1 ◁ C22×C3

311 conjugacy classes of subgroups; only the 20 normal subgroups are shown.

normal subgroups only

This group has 311 conjugacy classes of subgroups — too many to draw. Only its 20 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

72 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC22×C3×C5×GL(3,𝔽2), C22×C32×GL(3,𝔽2), C2×C3×D3×GL(3,𝔽2)
maximal normal subgroup ofC22×C3×C5×GL(3,𝔽2), C22×C32×GL(3,𝔽2)
maximal quotient ofC22×C3×C5×GL(3,𝔽2), C22×C32×GL(3,𝔽2), C2×C3×D3×GL(3,𝔽2)
automorphism group ofC23×C3×C7
outer automorphism group ofC23×C3×C7

GAP

Past the SmallGroups library coverage — no SmallGroups id.