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C3×#23779861 #44525149

order30861
automorphism?
homologyAbelianization (H1) = C34 · Schur multiplier (H2) = C35

Aliases

direct productC3×#23779861

Splittings

FittingC3×3−1+2×C127 ⋊ C3
SylowC127 ⋊ C3×#737

Subgroups

subgroupG/H
centerC32C32×C127⋊C3
commutator, cosocleC3×C127C34
FrattiniC3C33×C127⋊C3
FittingC3×3−1+2×C127C3
socleC32×C127C33
prime radicalC3×C32⋊(C127⋊C3)C3
hypercenterC3×3−1+2C127⋊C3
hypocenterC127C3×#737
LCSG ▷ C3×C127 ▷ C127
UCSC1 ◁ C32 ◁ C3×3−1+2

480 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, 303);