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C22×#17986809 #32911270

order18176
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C214

Aliases

direct productC22×#17986809

Splittings

FittingC22×AGL(1,ℤ/8)×C71 ⋊ C2
SylowC71 ⋊ C22×#577

Subgroups

subgroupG/H
centerC23C2×D4×D71
commutator, cosocleC4×C71C26
FrattiniC4C25×D71
FittingC22×AGL(1,ℤ/8)×C71C2
socleC23×C71C22×D4
hypercenterC22×AGL(1,ℤ/8)D71
hypocenterC71C22×#577
LCSG ▷ C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×AGL(1,ℤ/8)

11118 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, 1083386);