Finite Group Databasebeta

← Prev (#29469263) Next (#29469265) →

AGL(1,ℤ/8)×Dic118 #29469264

order15104
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productAGL(1,ℤ/8)×Dic118

Splittings

SylowC59 ⋊ Q8×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC22C22×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC4×AGL(1,ℤ/8)×C59C2
socleC22×C59C23×D4
prime radicalC2×AGL(1,ℤ/8)×C59C22
hypercenterC4×AGL(1,ℤ/8)D59
hypocenterC59Q8×AGL(1,ℤ/8)
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×AGL(1,ℤ/8)

2010 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

1331 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1050143);