Finite Group Databasebeta

← Prev (#46855981) Next (#46855983) →

C139×Dic7⋊C9 #46855982

order35028
automorphism?
homologyAbelianization (H1) = C4×C9×C139 · Schur multiplier (H2) = C1

Aliases

direct productC139×Dic7⋊C9
unambiguous semidirect productDic7⋊(C9×C139)
unambiguous semidirect product(C7⋊C9)⋊(C4×C139)

Splittings

derived, SylowC7 ⋊ C4×C9×C139
HallC7⋊C9×C139 ⋊ C4
HallDic7×C139 ⋊ C9
HallC7×C139 ⋊ C4×C9
HallC7⋊C9 ⋊ C4×C139
HallDic7 ⋊ C9×C139

Subgroups

subgroupG/H
center, hypercenterC2×C3×C139AGL(1,𝔽7)
commutator, hypocenterC7C4×C9×C139
FrattiniC2×C3AGL(1,𝔽7)×C139
Fitting, socle, prime radicalC2×C3×C7×C139C2×C3
cosocleC2×C3×C7C2×C3×C139
LCSG ▷ C7
UCSC1 ◁ C2×C3×C139

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 35028

Conjugacy classes & character table

5838 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35028, 18);