Finite Group Databasebeta

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C5×C9×#87938 #32911389

order18180
isoclinismisoclinic class of #87938
automorphism?
homologyAbelianization (H1) = C4×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC5×C9×#87938

Splittings

Fitting, HallC5×C9×C101 ⋊ C4
derived, SylowC101 ⋊ C4×C5×C9
HallC9×C101 ⋊ C4×C5
HallC5×C101 ⋊ C4×C9

Subgroups

subgroupG/H
center, hypercenterC5×C9#87938
commutator, hypocenterC101C4×C5×C9
FrattiniC3C3×C5×#87938
FittingC5×C9×C101C4
socleC3×C5×C101C3×C4
prime radicalC3×C5×D101C2×C3
cosocleC3×D101C2×C3×C5
LCSG ▷ C101
UCSC1 ◁ C5×C9

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4545

Conjugacy classes & character table

1305 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18180, 22);