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C7×GL(3,𝔽2) #11924297

order1176
isoclinismisoclinic class of GL(3,𝔽2)
automorphism?
homologyAbelianization (H1) = C7 · Schur multiplier (H2) = C2

Aliases

direct productC7×GL(3,𝔽2)

Subgroups

subgroupG/H
center, Fitting, hypercenterC7GL(3,𝔽2)
commutator, hypocenterGL(3,𝔽2)C7
FrattiniC1G
LCSG ▷ GL(3,𝔽2)
UCSC1 ◁ C7

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 49

Conjugacy classes & character table

42 conjugacy classes — view the full character table.

Relationships

derived subgroup ofC2×ΓL(1,𝔽8)×GL(3,𝔽2), #72244476, #72244479
socle of#72244476, #72244479
maximal subgroup ofΓL(1,𝔽8)×GL(3,𝔽2), C7×AGL(3,𝔽2), D7×GL(3,𝔽2), …
maximal normal subgroup ofΓL(1,𝔽8)×GL(3,𝔽2), D7×GL(3,𝔽2), C2×C7×GL(3,𝔽2), …
maximal quotient ofC7×AGL(3,𝔽2), C7×SL(2,𝔽7), C2×C7×GL(3,𝔽2)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1176, 212);