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Cayley diagram

D3×PSU(3,𝔽2) #89095

order432
isoclinismisoclinic class of D3×PSU(3,𝔽2)
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22×C3

Aliases

direct productD3×PSU(3,𝔽2)

Splittings

Fitting, socle, SylowC33 ⋊ C2×Q8

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, cosocleC3×C3⋊D3C23
Fitting, socle, hypocenterC33C2×Q8
prime radicalD3×C3⋊D3C22
LCSG ▷ C3×C3⋊D3 ▷ C33
UCSC1

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 12
transitive degreeμt(G) = 24

A minimal faithful permutation representation — 3 generators on 12 points:

(1,2,3)(4,7,8,9)(6,11,10,12);(5,7,8,12)(6,10,11,9);(2,3)

Conjugacy classes & character table

18 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×AΓL(1,𝔽9), C2×D3×PSU(3,𝔽2), D9×PSU(3,𝔽2), …
maximal normal subgroup ofD3×AΓL(1,𝔽9), C2×D3×PSU(3,𝔽2), D3×PSU(3,𝔽2)⋊C3, …
maximal quotient ofD3×#3777, Dic3×PSU(3,𝔽2), #11724148, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 742);