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C22×GL(3,𝔽2) #10621673

order672
isoclinismisoclinic class of GL(3,𝔽2)
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C22

Aliases

direct productC22×GL(3,𝔽2)

Subgroups

subgroupG/H
center, Fitting, hypercenterC22GL(3,𝔽2)
commutator, hypocenterGL(3,𝔽2)C22
FrattiniC1G
LCSG ▷ GL(3,𝔽2)
UCSC1 ◁ C22

143 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 28

Conjugacy classes & character table

24 conjugacy classes — view the full character table.

Relationships

socle ofC2×GL(3,𝔽2)⋊C4, C2×C4×GL(3,𝔽2), C22×SO(3,𝔽7)
maximal subgroup ofC2×GL(3,𝔽2)⋊C4, C22⋊SO(3,𝔽7), C2×C4×GL(3,𝔽2), …
maximal normal subgroup ofC2×GL(3,𝔽2)⋊C4, C22⋊SO(3,𝔽7), C2×C4×GL(3,𝔽2), …
maximal quotient ofC2×C4×GL(3,𝔽2), C2×#10621465, D4×GL(3,𝔽2), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(672, 1255);