Finite Group Databasebeta

← Prev (#34257684) Next (#34257686) →

AGL(1,ℤ/8)×C79⋊C8 #34257685

order20224
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productAGL(1,ℤ/8)×C79⋊C8

Splittings

SylowC79 ⋊ C8×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC2×C4C2×D4×D79
commutatorC4×C79C23×C8
FrattiniC42C23×D79
FittingC4×AGL(1,ℤ/8)×C79C2
socleC22×C79C2×C4×D4
prime radicalC2×AGL(1,ℤ/8)×C79C4
cosocleC42×C79C24
hypercenterC4×AGL(1,ℤ/8)D79
hypocenterC79C8×AGL(1,ℤ/8)
LCSG ▷ C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×AGL(1,ℤ/8)

802 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5056

Conjugacy classes & character table

1804 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 138984);