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SL(2,𝔽3)×C27 #10619567

order648
isoclinismisoclinic class of SL(2,𝔽3)
automorphism?
homologyAbelianization (H1) = C3×C27 · Schur multiplier (H2) = C3

Aliases

direct productSL(2,𝔽3)×C27

Splittings

FittingQ8×C27 ⋊ C3
derived, SylowQ8 ⋊ C3×C27

Subgroups

subgroupG/H
center, hypercenterC2×C27A4
commutator, hypocenterQ8C3×C27
FrattiniC2×C9C3×A4
FittingQ8×C27C3
socleC2×C3C9×A4
prime radicalC3×SL(2,𝔽3)C9
cosocleQ8×C9C32
LCSG ▷ Q8
UCSC1 ◁ C2×C27

46 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 216

Conjugacy classes & character table

189 conjugacy classes — view the full character table.

Relationships

derived subgroup ofC27⋊#226, C27⋊GL(2,𝔽3)
maximal subgroup ofC27×#226, C27×GL(2,𝔽3), C27⋊#226, …
maximal normal subgroup ofC27×#226, C27×GL(2,𝔽3), C27⋊#226, …
maximal quotient ofC2×SL(2,𝔽3)×C27, SL(2,𝔽3)×C81, C81⋊SL(2,𝔽3), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(648, 86);