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AGL(1,ℤ/8)×C71⋊C8 #31966868

order18176
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productAGL(1,ℤ/8)×C71⋊C8

Splittings

SylowC71 ⋊ C8×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC2×C4C2×D4×D71
commutatorC4×C71C23×C8
FrattiniC42C23×D71
FittingC4×AGL(1,ℤ/8)×C71C2
socleC22×C71C2×C4×D4
prime radicalC2×AGL(1,ℤ/8)×C71C4
cosocleC42×C71C24
hypercenterC4×AGL(1,ℤ/8)D71
hypocenterC71C8×AGL(1,ℤ/8)
LCSG ▷ C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×AGL(1,ℤ/8)

802 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4544

Conjugacy classes & character table

1628 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 138984);