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C22×#88410 #13147375

order1728
isoclinismisoclinic class of #1088
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C23

Aliases

direct productC22×#88410

Splittings

derived, SylowH(3,𝔽3) ⋊ C22×C16

Subgroups

subgroupG/H
center, hypercenterC22×C3×C4#157
commutator, hypocenterH(3,𝔽3)C22×C16
FrattiniC3×C4C22×#157
FittingC22×C4×H(3,𝔽3)C4
socleC23×C3#622
prime radicalC23×H(3,𝔽3)C8
cosocle#6180C23
LCSG ▷ H(3,𝔽3)
UCSC1 ◁ C22×C3×C4

299 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 576

Conjugacy classes & character table

224 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 13438);