Finite Group Databasebeta

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C5×C9×#10597010 #41001224

order26820
automorphism?
homologyAbelianization (H1) = C4×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC5×C9×#10597010

Splittings

Fitting, HallC5×C9×C149 ⋊ C4
derived, SylowC149 ⋊ C4×C5×C9
HallC9×C149 ⋊ C4×C5
HallC5×C149 ⋊ C4×C9

Subgroups

subgroupG/H
center, hypercenterC5×C9#10597010
commutator, hypocenterC149C4×C5×C9
FrattiniC3C3×C5×#10597010
FittingC5×C9×C149C4
socleC3×C5×C149C3×C4
prime radicalC3×C5×D149C2×C3
cosocleC3×D149C2×C3×C5
LCSG ▷ C149
UCSC1 ◁ C5×C9

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6705

Conjugacy classes & character table

1845 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26820, 10);