Finite Group Databasebeta

← Prev (#13094883) Next (#13094885) →

C32×GL(3,𝔽2) #13094884

order1512
isoclinismisoclinic class of GL(3,𝔽2)
automorphism?
homologyAbelianization (H1) = C32 · Schur multiplier (H2) = C2×C3

Aliases

direct productC32×GL(3,𝔽2)

Subgroups

subgroupG/H
center, Fitting, hypercenterC32GL(3,𝔽2)
commutator, hypocenterGL(3,𝔽2)C32
FrattiniC1G
LCSG ▷ GL(3,𝔽2)
UCSC1 ◁ C32

130 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 63

Conjugacy classes & character table

54 conjugacy classes — view the full character table.

Relationships

derived subgroup ofC3⋊D3×GL(3,𝔽2), #157×GL(3,𝔽2), C2×C3⋊D3×GL(3,𝔽2)
socle ofC3⋊D3×GL(3,𝔽2), #157×GL(3,𝔽2), C32×SO(3,𝔽7), …
maximal subgroup ofC32×C5×GL(3,𝔽2), C2×C32×GL(3,𝔽2), C3⋊D3×GL(3,𝔽2), …
maximal normal subgroup ofC32×C5×GL(3,𝔽2), C2×C32×GL(3,𝔽2), C3⋊D3×GL(3,𝔽2), …
maximal quotient ofC32×C5×GL(3,𝔽2), C2×C32×GL(3,𝔽2), C32×SL(2,𝔽7), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1512, 781);