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C2×C3×C22⋊C27 #10619785

order648
isoclinismisoclinic class of A4
automorphism?
homologyAbelianization (H1) = C2×C3×C27 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C3×C22⋊C27
unambiguous semidirect product(C23×C3)⋊C27

Splittings

derivedC22 ⋊ C2×C3×C27
SylowC23 ⋊ C3×C27

Subgroups

subgroupG/H
center, hypercenterC2×C3×C9A4
commutator, hypocenterC22C2×C3×C27
FrattiniC9C2×C3×A4
FittingC23×C3×C9C3
socle, prime radicalC23×C32C9
cosocleC22×C9C2×C32
LCSG ▷ C22
UCSC1 ◁ C2×C3×C9

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 162

Conjugacy classes & character table

216 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×(C22⋊C27)⋊C4, C3⋊((C22⋊C27)⋊C4), Dic3×C22⋊C27, …
maximal normal subgroup ofC3×(C22⋊C27)⋊C4, C3⋊((C22⋊C27)⋊C4), Dic3×C22⋊C27, …
maximal quotient ofC3×C4×C22⋊C27, C2×C3×Q8⋊C27, C3×#41⋊C27, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(648, 304);