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C22×D27⋊C3 #10619808

order648
isoclinismisoclinic class of D27⋊C3
automorphism?
homologyAbelianization (H1) = C23×C3 · Schur multiplier (H2) = C23

Aliases

direct productC22×D27⋊C3
unambiguous semidirect productD27⋊(C22×C3)
unambiguous semidirect product(C27⋊C3)⋊C23
unambiguous semidirect product(C2×C27⋊C3)⋊C22

Splittings

FittingC22×C27⋊C3 ⋊ C2
derivedC27 ⋊ C23×C3
SylowC27⋊C3 ⋊ C23

Subgroups

subgroupG/H
center, hypercenterC22D27⋊C3
commutator, cosocle, hypocenterC27C23×C3
FrattiniC9C22×C3×D3
FittingC22×C27⋊C3C2
socleC22×C3C3×D9
LCSG ▷ C27
UCSC1 ◁ C22

138 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 108

Conjugacy classes & character table

84 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(C2×D27⋊C3)⋊C4, C2×C4×D27⋊C3, C2×C4⋊(D27⋊C3), …
maximal normal subgroup of(C2×D27⋊C3)⋊C4, C2×C4×D27⋊C3, C2×C4⋊(D27⋊C3), …
maximal quotient ofC2×(C27⋊C3)⋊Q8, C2×C4×D27⋊C3, C2×C4⋊(D27⋊C3), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(648, 327);