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C2×C3×GL(3,𝔽2) #11759713

order1008
isoclinismisoclinic class of GL(3,𝔽2)
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×GL(3,𝔽2)

Subgroups

subgroupG/H
center, Fitting, hypercenterC2×C3GL(3,𝔽2)
commutator, hypocenterGL(3,𝔽2)C2×C3
FrattiniC1G
LCSG ▷ GL(3,𝔽2)
UCSC1 ◁ C2×C3

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 42

Conjugacy classes & character table

36 conjugacy classes — view the full character table.

Relationships

socle ofC3×C4×GL(3,𝔽2), C2×C3×SO(3,𝔽7), C2×C9×GL(3,𝔽2), …
maximal subgroup ofDic3×GL(3,𝔽2), SL(2,𝔽3)×GL(3,𝔽2), C2×C3×AGL(3,𝔽2), …
maximal normal subgroup ofDic3×GL(3,𝔽2), C2×C3×C5×GL(3,𝔽2), C2×C32×GL(3,𝔽2), …
maximal quotient ofC2×C3×AGL(3,𝔽2), AGL(1,𝔽7)×GL(3,𝔽2), C2×C3×C5×GL(3,𝔽2), …
automorphism group ofC23×C7, C23×C9
outer automorphism group ofC23×C7, C23×C9

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1008, 884);