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C2×AGL(1,ℤ/8)×#6923 #30625448

order15616
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×AGL(1,ℤ/8)×#6923
unambiguous semidirect productD61⋊(C4×AGL(1,ℤ/8))

Splittings

FittingC2×AGL(1,ℤ/8)×C61 ⋊ C4
SylowC61 ⋊ C2×C4×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC22C2×D4×#6923
commutatorC4×C61C24×C4
FrattiniC4C24×#6923
FittingC2×AGL(1,ℤ/8)×C61C4
socleC22×C61C2×C4×D4
prime radicalC2×AGL(1,ℤ/8)×D61C2
cosocleC4×D61C25
hypercenterC2×AGL(1,ℤ/8)#6923
hypocenterC61C2×C4×AGL(1,ℤ/8)
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

3242 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 976

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1115003);