Finite Group Databasebeta

C2×D7⋊C9×C127 #44544664

order32004
automorphism?
homologyAbelianization (H1) = C22×C9×C127 · Schur multiplier (H2) = C2

Aliases

direct productC2×D7⋊C9×C127
unambiguous semidirect productD7⋊(C2×C9×C127)
unambiguous semidirect product(C2×D7)⋊(C9×C127)
unambiguous semidirect product(C7⋊C9)⋊(C22×C127)
unambiguous semidirect product(C2×C7⋊C9)⋊(C2×C127)

Splittings

derived, SylowC7 ⋊ C22×C9×C127
HallC7⋊C9×C127 ⋊ C22
HallC2×D7×C127 ⋊ C9
HallC7×C127 ⋊ C22×C9
HallC7⋊C9 ⋊ C22×C127
HallC2×D7 ⋊ C9×C127

Subgroups

subgroupG/H
center, hypercenterC2×C3×C127AGL(1,𝔽7)
commutator, hypocenterC7C22×C9×C127
FrattiniC3C2×AGL(1,𝔽7)×C127
Fitting, socleC2×C3×C7×C127C2×C3
prime radicalC2×C3×D7×C127C3
cosocleC3×C7C22×C3×C127
LCSG ▷ C7
UCSC1 ◁ C2×C3×C127

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16002

Conjugacy classes & character table

5334 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32004, 46);