Finite Group Databasebeta

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C3×C7×Dic3×C137 #46828614

order34524
automorphism?
homologyAbelianization (H1) = C3×C4×C7×C137 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7×Dic3×C137
unambiguous semidirect productC3⋊(C3×C4×C7×C137)

Splittings

derivedC3 ⋊ C3×C4×C7×C137
HallC32×C7×C137 ⋊ C4
HallC32×C137 ⋊ C4×C7
HallC32×C7 ⋊ C4×C137
SylowC32 ⋊ C4×C7×C137

Subgroups

subgroupG/H
center, hypercenterC2×C3×C7×C137D3
commutator, hypocenterC3C3×C4×C7×C137
FrattiniC2C3×D3×C7×C137
Fitting, socle, prime radicalC2×C32×C7×C137C2
cosocleC2×C3C2×C3×C7×C137
LCSG ▷ C3
UCSC1 ◁ C2×C3×C7×C137

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11508

Conjugacy classes & character table

17262 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34524, 57);