Finite Group Databasebeta

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#37555922

order23571
automorphism?
homologyAbelianization (H1) = C33 · Schur multiplier (H2) = C3

Aliases

No aliases for this group.

Splittings

SylowC97 ⋊ #6900

Subgroups

subgroupG/H
center, FrattiniC32C32×C97⋊C3
commutator, socle, cosocleC32×C97C33
FittingC3×3−1+2×C97C3
prime radicalC33×C97C32
hypercenterC3×3−1+2C97⋊C3
hypocenterC97#6900
LCSG ▷ C32×C97 ▷ C97
UCSC1 ◁ C32 ◁ C3×3−1+2

140 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7857

Polycyclic presentation:

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

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, 229);