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C23×#6180 #13154405

order1728
isoclinismisoclinic class of #272
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC23×#6180

Splittings

derived, SylowH(3,𝔽3) ⋊ C23×C8

Subgroups

subgroupG/H
center, hypercenterC23×C3×C4C3⋊D3
commutator, hypocenterH(3,𝔽3)C23×C8
FrattiniC3×C4C23×C3⋊D3
FittingC23×C4×H(3,𝔽3)C2
socleC24×C3C3⋊Dic3
prime radicalC24×H(3,𝔽3)C4
cosocleC4×H(3,𝔽3)C24
LCSG ▷ H(3,𝔽3)
UCSC1 ◁ C23×C3×C4

1859 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 576

Conjugacy classes & character table

320 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 20468);