Finite Group Databasebeta

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3−1+2×#11765919 #44525198

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

Aliases

direct product3−1+2×#11765919

Splittings

Fitting3−1+2×C127 ⋊ C9
SylowC127 ⋊ C9×3−1+2

Subgroups

subgroupG/H
center, FrattiniC3C32×#11765919
commutator, socleC3×C127C32×C9
Fitting3−1+2×C127C9
prime radicalC32×C127⋊C3C32
cosocleC3×C127⋊C3C33
hypercenter3−1+2#11765919
hypocenterC127C9×3−1+2
LCSG ▷ C3×C127 ▷ C127
UCSC1 ◁ C3 ◁ 3−1+2

148 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1143

Conjugacy classes & character table

253 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30861, 352);