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AGL(1,ℤ/8)×#10597010 #34061446

order19072
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productAGL(1,ℤ/8)×#10597010

Splittings

FittingAGL(1,ℤ/8)×C149 ⋊ C4
SylowC149 ⋊ C4×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC2C2×D4×#10597010
commutatorC4×C149C23×C4
FrattiniC4C23×#10597010
FittingAGL(1,ℤ/8)×C149C4
socleC2×C149C2×C4×D4
prime radicalAGL(1,ℤ/8)×D149C2
cosocleC4×D149C24
hypercenterAGL(1,ℤ/8)#10597010
hypocenterC149C4×AGL(1,ℤ/8)
LCSG ▷ C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

548 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1192

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19072, 21265);