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C4×PSU(3,𝔽2)⋊C3 #11724087

order864
isoclinismisoclinic class of PSU(3,𝔽2)⋊C3
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C3

Aliases

direct productC4×PSU(3,𝔽2)⋊C3
unambiguous semidirect product(C4×PSU(3,𝔽2))⋊C3

Splittings

FittingC32×C4 ⋊ SL(2,𝔽3)
derivedPSU(3,𝔽2) ⋊ C3×C4

Subgroups

subgroupG/H
center, hypercenterC4PSU(3,𝔽2)⋊C3
commutator, hypocenterPSU(3,𝔽2)C3×C4
FrattiniC2C2×PSU(3,𝔽2)⋊C3
FittingC32×C4SL(2,𝔽3)
socleC2×C32C2×SL(2,𝔽3)
prime radicalC2×PSU(3,𝔽2)⋊C3C2
cosocleC2×PSU(3,𝔽2)C2×C3
LCSG ▷ PSU(3,𝔽2)
UCSC1 ◁ C4

82 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 13
transitive degreeμt(G) = 36

Conjugacy classes & character table

40 conjugacy classes — view the full character table.

Relationships

derived subgroup of#72245046, C2×#72220122, #72245256, …
maximal subgroup of(PSU(3,𝔽2)⋊C3)⋊C8, C8×PSU(3,𝔽2)⋊C3, (PSU(3,𝔽2)⋊C3)⋊Q8, …
maximal normal subgroup of(PSU(3,𝔽2)⋊C3)⋊C8, C8×PSU(3,𝔽2)⋊C3, (PSU(3,𝔽2)⋊C3)⋊Q8, …
maximal quotient ofC8×PSU(3,𝔽2)⋊C3, C2×C4×PSU(3,𝔽2)⋊C3, #72213336, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(864, 4054);