Finite Group Databasebeta

C2×#22589508 #32024853

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

Aliases

direct productC2×#22589508

Splittings

SylowC71 ⋊ C2×#2030

Subgroups

subgroupG/H
centerC23#14556098
commutator, cosocleC24×C71C24
FrattiniC24C23×D71
FittingC2×#342×C71C2
socleC23×C71#120
prime radicalC25×C71C23
hypercenterC2×#342D71
hypocenterC71C2×#2030
LCSG ▷ C24×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C25 ◁ C2×#342

1482 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4544

Conjugacy classes & character table

1592 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 196969);