Finite Group Databasebeta

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3−1+2×C97⋊C9 #37555868

order23571
automorphism?
homologyAbelianization (H1) = C32×C9 · Schur multiplier (H2) = C32

Aliases

direct product3−1+2×C97⋊C9

Splittings

SylowC97 ⋊ C9×3−1+2

Subgroups

subgroupG/H
center, FrattiniC32C32×C97⋊C3
commutatorC3×C97C32×C9
FittingC3×3−1+2×C97C3
socle, cosocleC32×C97C33
prime radicalC33×C97C32
hypercenterC3×3−1+2C97⋊C3
hypocenterC97C9×3−1+2
LCSG ▷ C3×C97 ▷ C97
UCSC1 ◁ C32 ◁ C3×3−1+2

148 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7857

Conjugacy classes & character table

1155 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23571, 175);