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C2×#11720310 #13139960

order1728
isoclinismisoclinic class of ((C3⋊D3)⋊C3)⋊C2
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct productC2×#11720310

Splittings

derived, SylowH(3,𝔽3) ⋊ C2×C4×C8

Subgroups

subgroupG/H
center, hypercenterC22×C4((C3⋊D3)⋊C3)⋊C2
commutator, hypocenterH(3,𝔽3)C2×C4×C8
FrattiniC2×C3×C4C2×D32
FittingC22×C4×H(3,𝔽3)C22
socleC23×C3D3×Dic3
prime radicalC23×H(3,𝔽3)C2×C4
cosocleC2×C4×H(3,𝔽3)C23
LCSG ▷ H(3,𝔽3)
UCSC1 ◁ C22×C4

643 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 576

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 6023);