Finite Group Databasebeta

C2×#22589517 #32024890

order18176
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#22589517

Splittings

SylowC71 ⋊ C2×#2032

Subgroups

subgroupG/H
centerC22#17985911
commutator, cosocleC24×C71C24
FrattiniC24C23×D71
FittingC22×#99×C71C2
socleC22×C71#393
prime radicalC23×D4×C71C22
hypercenterC22×#99D71
hypocenterC71C2×#2032
LCSG ▷ C24×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C25 ◁ C22×#99

1434 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2272

Conjugacy classes & character table

1586 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 197006);