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C3×3−1+2⋊(C31⋊C9) #36381016

order22599
automorphism?
homologyAbelianization (H1) = C32×C9 · Schur multiplier (H2) = C33

Aliases

direct productC3×3−1+2⋊(C31⋊C9)

Splittings

SylowC31 ⋊ C3×3−1+2⋊C9

Subgroups

subgroupG/H
centerC33C32⋊(C31⋊C3)
commutatorC32×C31C32×C9
FrattiniC33C32×C31⋊C3
FittingC32×3−1+2×C31C3
socleC33×C31H(3,𝔽3)
prime radicalC34×C31C32
cosocleC33×C31C33
hypercenterC32×3−1+2C31⋊C3
hypocenterC31C3×3−1+2⋊C9
LCSG ▷ C32×C31 ▷ C3×C31 ▷ C31
UCSC1 ◁ C33 ◁ C34 ◁ C32×3−1+2

572 conjugacy classes of subgroups; only the 166 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 166 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7533

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, 2037);