Finite Group Databasebeta

← Prev (#46856072) Next (#46856074) →

C3×C7×Dic3×C139 #46856073

order35028
automorphism?
homologyAbelianization (H1) = C3×C4×C7×C139 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7×Dic3×C139
unambiguous semidirect productC3⋊(C3×C4×C7×C139)

Splittings

derivedC3 ⋊ C3×C4×C7×C139
HallC32×C7×C139 ⋊ C4
HallC32×C139 ⋊ C4×C7
HallC32×C7 ⋊ C4×C139
SylowC32 ⋊ C4×C7×C139

Subgroups

subgroupG/H
center, hypercenterC2×C3×C7×C139D3
commutator, hypocenterC3C3×C4×C7×C139
FrattiniC2C3×D3×C7×C139
Fitting, socle, prime radicalC2×C32×C7×C139C2
cosocleC2×C3C2×C3×C7×C139
LCSG ▷ C3
UCSC1 ◁ C2×C3×C7×C139

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11676

Conjugacy classes & character table

17514 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35028, 109);