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C3×H(3,𝔽3)×C97⋊C3 #37555987

order23571
automorphism?
homologyAbelianization (H1) = C34 · Schur multiplier (H2) = C37

Aliases

direct productC3×H(3,𝔽3)×C97⋊C3

Splittings

FittingC3×H(3,𝔽3)×C97 ⋊ C3
SylowC97 ⋊ C32×H(3,𝔽3)

Subgroups

subgroupG/H
centerC32C32×C97⋊C3
commutator, cosocleC3×C97C34
FrattiniC3C33×C97⋊C3
FittingC3×H(3,𝔽3)×C97C3
socleC32×C97C33
hypercenterC3×H(3,𝔽3)C97⋊C3
hypocenterC97C32×H(3,𝔽3)
LCSG ▷ C3×C97 ▷ C97
UCSC1 ◁ C32 ◁ C3×H(3,𝔽3)

900 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2619

Conjugacy classes & character table

1155 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23571, 294);