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H(3,𝔽3)×#11765917 #44525015

order30861
automorphism?
homologyAbelianization (H1) = C32×C9 · Schur multiplier (H2) = C34

Aliases

direct productH(3,𝔽3)×#11765917

Splittings

SylowC127 ⋊ C9×H(3,𝔽3)

Subgroups

subgroupG/H
center, FrattiniC32C32×C127⋊C3
commutatorC3×C127C32×C9
Fitting, prime radicalC3×H(3,𝔽3)×C127C3
socle, cosocleC32×C127C33
hypercenterC3×H(3,𝔽3)C127⋊C3
hypocenterC127C9×H(3,𝔽3)
LCSG ▷ C3×C127 ▷ C127
UCSC1 ◁ C32 ◁ C3×H(3,𝔽3)

202 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10287

Conjugacy classes & character table

1485 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30861, 169);