Finite Group Databasebeta

#41005087

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

Aliases

No aliases for this group.

Splittings

SylowC37 ⋊ #10624544

Subgroups

subgroupG/H
centerC32×C9C3×C37⋊C3
commutatorC3×C37C3×C92
FrattiniC33C32×C37⋊C3
FittingC3×C92×C37C3
socle, prime radical, cosocleC33×C37C33
hypercenterC3×C92C37⋊C3
hypocenterC37#10624544
LCSG ▷ C3×C37 ▷ C37
UCSC1 ◁ C32×C9 ◁ C3×C92

440 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 26973

Polycyclic presentation:

3^6,37|a^3=e,b^3=f,c^3=d,b^a=bd,g^b=g^26

Conjugacy classes & character table

3213 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26973, 858);