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C4×#17986170 #32003344

order18176
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC4×#17986170

Splittings

FittingC4×AGL(1,ℤ/8)×C71 ⋊ C2
SylowC71 ⋊ C4×#454

Subgroups

subgroupG/H
centerC2×C4#14556096
commutatorC2×C4×C71C23×C4
FrattiniC22×C4C23×D71
FittingC4×AGL(1,ℤ/8)×C71C2
socleC22×C71C2×#120
prime radicalC2×#17986170C2
cosocleC22×C4×C71C24
hypercenterC4×AGL(1,ℤ/8)D71
hypocenterC71C4×#454
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×AGL(1,ℤ/8)

1390 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4544

Conjugacy classes & character table

1604 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 175460);