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C2×#11721824 #13154409

order1728
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC2×#11721824

Splittings

SylowH(3,𝔽3) ⋊ C2×C22⋊Q8

Subgroups

subgroupG/H
center, socleC23×C3C22×C3⋊D3
commutator, cosocleC22×H(3,𝔽3)C24
FrattiniC22×C3C23×C3⋊D3
FittingC23×C4×H(3,𝔽3)C2
prime radicalC24×H(3,𝔽3)C22
hypercenterC23×C3×C4C3⋊D3
hypocenterH(3,𝔽3)C2×C22⋊Q8
LCSG ▷ C22×H(3,𝔽3) ▷ H(3,𝔽3)
UCSC1 ◁ C23×C3 ◁ C23×C3×C4

1771 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 288

Conjugacy classes & character table

212 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 20472);