Finite Group Databasebeta

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C7×C9×#10587739 #46828577

order34524
automorphism?
homologyAbelianization (H1) = C4×C7×C9 · Schur multiplier (H2) = C1

Aliases

direct productC7×C9×#10587739

Splittings

Fitting, HallC7×C9×C137 ⋊ C4
derived, SylowC137 ⋊ C4×C7×C9
HallC9×C137 ⋊ C4×C7
HallC7×C137 ⋊ C4×C9

Subgroups

subgroupG/H
center, hypercenterC7×C9#10587739
commutator, hypocenterC137C4×C7×C9
FrattiniC3C3×C7×#10587739
FittingC7×C9×C137C4
socleC3×C7×C137C3×C4
prime radicalC3×C7×D137C2×C3
cosocleC3×D137C2×C3×C7
LCSG ▷ C137
UCSC1 ◁ C7×C9

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8631

Conjugacy classes & character table

2394 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34524, 20);