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C23×SU(3,𝔽2) #13180077

order1728
isoclinismisoclinic class of SU(3,𝔽2)
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC23×SU(3,𝔽2)

Splittings

FittingC23×H(3,𝔽3) ⋊ Q8
SylowH(3,𝔽3) ⋊ C23×Q8

Subgroups

subgroupG/H
center, socle, hypercenterC23×C3PSU(3,𝔽2)
commutator, cosocle#272C25
FrattiniC3C23×PSU(3,𝔽2)
FittingC23×H(3,𝔽3)Q8
prime radicalC23×#272C22
hypocenterH(3,𝔽3)C23×Q8
LCSG ▷ #272 ▷ H(3,𝔽3)
UCSC1 ◁ C23×C3

1409 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 216

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC23×#6249⋊C2
maximal normal subgroup ofC23×#6249⋊C2

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 46140);