Finite Group Databasebeta

C2×#22589610 #32025279

order18176
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#22589610

Splittings

SylowC71 ⋊ C2×#2048

Subgroups

subgroupG/H
centerC22#17985913
commutator, cosocleC22×C4×C71C24
FrattiniC22×C4C23×D71
Fitting, prime radicalC22×AGL(1,ℤ/8)×C71C2
socleC22×C71#394
hypercenterC22×AGL(1,ℤ/8)D71
hypocenterC71C2×#2048
LCSG ▷ C22×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×AGL(1,ℤ/8)

1450 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2272

Conjugacy classes & character table

1586 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 197395);