Finite Group Databasebeta

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3−1+2×C367⋊C3 #44446221

order29727
automorphism?
homologyAbelianization (H1) = C33 · Schur multiplier (H2) = C32

Aliases

direct product3−1+2×C367⋊C3

Splittings

Fitting3−1+2×C367 ⋊ C3
SylowC367 ⋊ C3×3−1+2

Subgroups

subgroupG/H
center, FrattiniC3C32×C367⋊C3
commutator, socle, cosocleC3×C367C33
Fitting3−1+2×C367C3
prime radicalC32×C367⋊C3C3
hypercenter3−1+2C367⋊C3
hypocenterC367C3×3−1+2
LCSG ▷ C3×C367 ▷ C367
UCSC1 ◁ C3 ◁ 3−1+2

76 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3303

Conjugacy classes & character table

1375 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29727, 42);