Finite Group Databasebeta

C32×D7×D139 #46856151

order35028
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3

Aliases

direct productC32×D7×D139

Splittings

Fitting, socle, HallC32×C7×C139 ⋊ C22
derived, HallC7×C139 ⋊ C22×C32
HallC32×C139 ⋊ C2×D7
SylowC139 ⋊ C2×C32×D7
HallC32×C7 ⋊ C2×D139
SylowC7 ⋊ C2×C32×D139

Subgroups

subgroupG/H
center, hypercenterC32D7×D139
commutator, cosocle, hypocenterC7×C139C22×C32
FrattiniC1G
Fitting, socleC32×C7×C139C22
LCSG ▷ C7×C139
UCSC1 ◁ C32

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8757

Conjugacy classes & character table

3195 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35028, 187);