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C8×SU(3,𝔽2) #13146709

order1728
isoclinismisoclinic class of SU(3,𝔽2)
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C22

Aliases

direct productC8×SU(3,𝔽2)

Splittings

FittingC8×H(3,𝔽3) ⋊ Q8
SylowH(3,𝔽3) ⋊ C8×Q8

Subgroups

subgroupG/H
center, hypercenterC3×C8PSU(3,𝔽2)
commutator#272C22×C8
FrattiniC3×C4C2×PSU(3,𝔽2)
FittingC8×H(3,𝔽3)Q8
socleC2×C3C4×PSU(3,𝔽2)
prime radicalC2×#272C22×C4
cosocleC4×#272C23
hypocenterH(3,𝔽3)C8×Q8
LCSG ▷ #272 ▷ H(3,𝔽3)
UCSC1 ◁ C3×C8

175 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 216

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 12772);