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H(3,𝔽3)×C97⋊C9 #37555862

order23571
automorphism?
homologyAbelianization (H1) = C32×C9 · Schur multiplier (H2) = C34

Aliases

direct productH(3,𝔽3)×C97⋊C9

Splittings

SylowC97 ⋊ C9×H(3,𝔽3)

Subgroups

subgroupG/H
center, FrattiniC32C32×C97⋊C3
commutatorC3×C97C32×C9
Fitting, prime radicalC3×H(3,𝔽3)×C97C3
socle, cosocleC32×C97C33
hypercenterC3×H(3,𝔽3)C97⋊C3
hypocenterC97C9×H(3,𝔽3)
LCSG ▷ C3×C97 ▷ C97
UCSC1 ◁ C32 ◁ C3×H(3,𝔽3)

202 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7857

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, 169);