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C2×SL(3,𝔽3) #72210858

order11232
isoclinismisoclinic class of SL(3,𝔽3)
automorphism?
homologyAbelianization (H1) = C2 · Schur multiplier (H2) = C1

Aliases

general linearGL(3,𝔽3)
direct productC2×SL(3,𝔽3)

Subgroups

subgroupG/H
center, Fitting, hypercenterC2SL(3,𝔽3)
commutator, hypocenterSL(3,𝔽3)C2
FrattiniC1G
LCSG ▷ SL(3,𝔽3)
UCSC1 ◁ C2

154 conjugacy classes of subgroups; only the 4 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 4 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

24 conjugacy classes — view the full character table.

Relationships

socle ofC4×SL(3,𝔽3)
maximal subgroup ofC22×SL(3,𝔽3), C4×SL(3,𝔽3)
maximal normal subgroup ofC22×SL(3,𝔽3), C4×SL(3,𝔽3)
maximal quotient ofC22×SL(3,𝔽3), C4×SL(3,𝔽3)
automorphism group ofC33, C2×C33
outer automorphism group ofC33, C2×C33

GAP

Past the SmallGroups library coverage — no SmallGroups id.