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C2×C3×SU(3,𝔽2) #13049262

order1296
isoclinismisoclinic class of SU(3,𝔽2)
automorphism?
homologyAbelianization (H1) = C23×C3 · Schur multiplier (H2) = C22

Aliases

direct productC2×C3×SU(3,𝔽2)

Splittings

FittingC2×C3×H(3,𝔽3) ⋊ Q8
SylowC3×H(3,𝔽3) ⋊ C2×Q8

Subgroups

subgroupG/H
center, socle, hypercenterC2×C32PSU(3,𝔽2)
commutator, cosocle#272C23×C3
FrattiniC3C2×C3×PSU(3,𝔽2)
FittingC2×C3×H(3,𝔽3)Q8
prime radicalC2×C3×#272C22
hypocenterH(3,𝔽3)C2×C3×Q8
LCSG ▷ #272 ▷ H(3,𝔽3)
UCSC1 ◁ C2×C32

188 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 162

Conjugacy classes & character table

96 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1296, 2980);