Finite Group Databasebeta

← Prev (#33999772) Next (#33999774) →

C22×AGL(1,ℤ/8)×D73 #33999773

order18688
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C214

Aliases

direct productC22×AGL(1,ℤ/8)×D73

Splittings

FittingC22×AGL(1,ℤ/8)×C73 ⋊ C2
SylowC73 ⋊ C23×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC4×C73C26
FrattiniC4C25×D73
FittingC22×AGL(1,ℤ/8)×C73C2
socleC23×C73C22×D4
hypercenterC22×AGL(1,ℤ/8)D73
hypocenterC73C23×AGL(1,ℤ/8)
LCSG ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×AGL(1,ℤ/8)

13310 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2336

Conjugacy classes & character table

1672 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 1083357);