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#36376237

order22437
automorphism?
homologyAbelianization (H1) = C32 · Schur multiplier (H2) = C3

Aliases

No aliases for this group.

Splittings

Fitting3−1+2×C277 ⋊ C3
SylowC277 ⋊ AΣL(1,𝔽27)

Subgroups

subgroupG/H
centerC3C32⋊(C277⋊C3)
commutator, cosocleC32×C277C32
FrattiniC32C3×C277⋊C3
Fitting3−1+2×C277C3
socleC3×C277H(3,𝔽3)
hypercenter3−1+2C277⋊C3
hypocenterC277AΣL(1,𝔽27)
LCSG ▷ C32×C277 ▷ C3×C277 ▷ C277
UCSC1 ◁ C3 ◁ C32 ◁ 3−1+2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2493

Polycyclic presentation:

3^4,277|b^a=bc,c^a=cd,e^a=e^160,e^b=e^116

Conjugacy classes & character table

1029 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22437, 30);