Finite Group Databasebeta

C37⋊C3×#6855 #41005084

order26973
automorphism?
homologyAbelianization (H1) = C3×C92 · Schur multiplier (H2) = C35

Aliases

direct productC37⋊C3×#6855

Splittings

FittingC37×#6855 ⋊ C3
SylowC37 ⋊ C3×#6855

Subgroups

subgroupG/H
center, FrattiniC33C32×C37⋊C3
commutatorC3×C37C3×C92
FittingC37×#6855C3
socle, cosocleC33×C37C33
prime radicalC33×C37⋊C3C32
hypercenter#6855C37⋊C3
hypocenterC37C3×#6855
LCSG ▷ C3×C37 ▷ C37
UCSC1 ◁ C33 ◁ #6855

1052 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8991

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(26973, 855);