Finite Group Databasebeta

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#41007613

order26973
automorphism?
homologyAbelianization (H1) = C34 · Schur multiplier (H2) = C34

Aliases

No aliases for this group.

Splittings

FittingC9×3−1+2×C37 ⋊ C3
SylowC37 ⋊ #10624877

Subgroups

subgroupG/H
centerC3×C9C32×C37⋊C3
commutator, socle, cosocleC32×C37C34
FrattiniC32C33×C37⋊C3
FittingC9×3−1+2×C37C3
prime radicalC3×C32⋊(C37⋊C3)C32
hypercenterC9×3−1+2C37⋊C3
hypocenterC37#10624877
LCSG ▷ C32×C37 ▷ C37
UCSC1 ◁ C3×C9 ◁ C9×3−1+2

662 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8991

Polycyclic presentation:

3^6,37|b^3=f,d^3=e,b^a=be,c^a=cf,g^b=g^10,g^c=g^26

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, 3384);