Finite Group Databasebeta

← Prev (#32004312) Next (#32004314) →

C4×#17986260 #32004313

order18176
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4×#17986260

Splittings

SylowC71 ⋊ C4×#471

Subgroups

subgroupG/H
centerC2×C4#14556100
commutatorC2×C4×C71C23×C4
FrattiniC22×C4C23×D71
FittingC4×AGL(1,ℤ/8)×C71C2
socleC22×C71C2×#121
prime radicalC2×AGL(1,ℤ/8)×C71C22
cosocleC22×C4×C71C24
hypercenterC4×AGL(1,ℤ/8)D71
hypocenterC71C4×#471
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×AGL(1,ℤ/8)

914 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, 176429);