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3−1+2⋊(C97⋊C9) #37555800

order23571
automorphism?
homologyAbelianization (H1) = C3×C9 · Schur multiplier (H2) = C3

Aliases

unambiguous semidirect product3−1+2⋊(C97⋊C9)

Splittings

SylowC97 ⋊ 3−1+2⋊C9

Subgroups

subgroupG/H
centerC32C32⋊(C97⋊C3)
commutatorC32×C97C3×C9
FrattiniC33C3×C97⋊C3
FittingC3×3−1+2×C97C3
socleC32×C97H(3,𝔽3)
prime radical, cosocleC33×C97C32
hypercenterC3×3−1+2C97⋊C3
hypocenterC973−1+2⋊C9
LCSG ▷ C32×C97 ▷ C3×C97 ▷ C97
UCSC1 ◁ C32 ◁ C33 ◁ C3×3−1+2

82 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7857

Polycyclic presentation:

3^5,97|a^3=d,b^3=e,b^a=bc,c^a=ce,f^a=f^35,c^b=ce

Conjugacy classes & character table

1107 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23571, 107);