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#36382363

order22599
automorphism?
homologyAbelianization (H1) = C34 · Schur multiplier (H2) = C34

Aliases

No aliases for this group.

Splittings

FittingC9×3−1+2×C31 ⋊ C3
SylowC31 ⋊ #10624877

Subgroups

subgroupG/H
centerC3×C9C32×C31⋊C3
commutator, socle, cosocleC32×C31C34
FrattiniC32C33×C31⋊C3
FittingC9×3−1+2×C31C3
prime radicalC3×C32⋊(C31⋊C3)C32
hypercenterC9×3−1+2C31⋊C3
hypocenterC31#10624877
LCSG ▷ C32×C31 ▷ C31
UCSC1 ◁ C3×C9 ◁ C9×3−1+2

662 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7533

Polycyclic presentation:

3^6,31|b^3=f,d^3=e,b^a=be,c^a=cf,g^b=g^5,g^c=g^25

Conjugacy classes & character table

1143 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22599, 3384);