Finite Group Databasebeta

C37⋊C3×#6862 #41005307

order26973
automorphism?
homologyAbelianization (H1) = C33 · Schur multiplier (H2) = C33

Aliases

direct productC37⋊C3×#6862

Splittings

FittingC37×#6862 ⋊ C3
SylowC37 ⋊ C3×#6862

Subgroups

subgroupG/H
centerC32H(3,𝔽3)×C37⋊C3
commutator, cosocleC33×C37C33
FrattiniC33C32×C37⋊C3
FittingC37×#6862C3
socleC32×C37C3×H(3,𝔽3)
prime radicalC33×C37⋊C3C32
hypercenter#6862C37⋊C3
hypocenterC37C3×#6862
LCSG ▷ C33×C37 ▷ C32×C37 ▷ C37
UCSC1 ◁ C32 ◁ C33 ◁ #6862

284 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2997

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26973, 1078);