Finite Group Databasebeta

#41006216

order26973
automorphism?
homologyAbelianization (H1) = C32×C9 · Schur multiplier (H2) = C33

Aliases

No aliases for this group.

Splittings

SylowC37 ⋊ #10624684

Subgroups

subgroupG/H
center, FrattiniC3×C9C32×C37⋊C3
commutator, socleC32×C37C32×C9
FittingC3×C37×#737C3
prime radicalC3×H(3,𝔽3)×C37C9
cosocleC3×C9×C37C33
hypercenterC3×#737C37⋊C3
hypocenterC37#10624684
LCSG ▷ C32×C37 ▷ C37
UCSC1 ◁ C3×C9 ◁ C3×#737

332 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8991

Polycyclic presentation:

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

Conjugacy classes & character table

1341 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26973, 1987);