Finite Group Databasebeta

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C4×AGL(1,ℤ/8)×D59 #29452745

order15104
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC4×AGL(1,ℤ/8)×D59

Splittings

FittingC4×AGL(1,ℤ/8)×C59 ⋊ C2
SylowC59 ⋊ C2×C4×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC2×C4C2×D4×D59
commutatorC4×C59C24×C4
FrattiniC2×C4C24×D59
FittingC4×AGL(1,ℤ/8)×C59C2
socleC22×C59C23×D4
prime radicalC2×AGL(1,ℤ/8)×D59C2
cosocleC2×C4×C59C25
hypercenterC4×AGL(1,ℤ/8)D59
hypocenterC59C2×C4×AGL(1,ℤ/8)
LCSG ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×AGL(1,ℤ/8)

3242 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1888

Conjugacy classes & character table

1364 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1033624);