Finite Group Databasebeta

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C4×AGL(1,ℤ/8)×D61 #30544069

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

Aliases

direct productC4×AGL(1,ℤ/8)×D61

Splittings

FittingC4×AGL(1,ℤ/8)×C61 ⋊ C2
SylowC61 ⋊ C2×C4×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC2×C4C2×D4×D61
commutatorC4×C61C24×C4
FrattiniC2×C4C24×D61
FittingC4×AGL(1,ℤ/8)×C61C2
socleC22×C61C23×D4
prime radicalC2×AGL(1,ℤ/8)×D61C2
cosocleC2×C4×C61C25
hypercenterC4×AGL(1,ℤ/8)D61
hypocenterC61C2×C4×AGL(1,ℤ/8)
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×AGL(1,ℤ/8)

3242 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1952

Conjugacy classes & character table

1408 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1033624);