Finite Group Databasebeta

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C137×Dic63 #46828565

order34524
automorphism?
homologyAbelianization (H1) = C4×C137 · Schur multiplier (H2) = C1

Aliases

direct productC137×Dic63
unambiguous semidirect productC7⋊(Dic9×C137)
unambiguous semidirect productC9⋊(Dic7×C137)

Splittings

derived, HallC7×C9 ⋊ C4×C137
HallC7×C9×C137 ⋊ C4
HallC9×C137 ⋊ Dic7
HallC7×C137 ⋊ Dic9
SylowC9 ⋊ Dic7×C137
SylowC7 ⋊ Dic9×C137

Subgroups

subgroupG/H
center, hypercenterC2×C137D63
commutator, hypocenterC7×C9C4×C137
FrattiniC2×C3D21×C137
FittingC2×C7×C9×C137C2
socle, prime radicalC2×C3×C7×C137D3
cosocleC2×C7×C9C2×C137
LCSG ▷ C7×C9
UCSC1 ◁ C2×C137

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 34524

Conjugacy classes & character table

9042 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34524, 8);