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AGL(1,ℤ/8)×C59⋊C8 #28558105

order15104
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productAGL(1,ℤ/8)×C59⋊C8

Splittings

SylowC59 ⋊ C8×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC2×C4C2×D4×D59
commutatorC4×C59C23×C8
FrattiniC42C23×D59
FittingC4×AGL(1,ℤ/8)×C59C2
socleC22×C59C2×C4×D4
prime radicalC2×AGL(1,ℤ/8)×C59C4
cosocleC42×C59C24
hypercenterC4×AGL(1,ℤ/8)D59
hypocenterC59C8×AGL(1,ℤ/8)
LCSG ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×AGL(1,ℤ/8)

802 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

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, 138984);