Finite Group Databasebeta

C2×#22589856 #32027199

order18176
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC2×#22589856

Splittings

SylowC71 ⋊ C2×#2091

Subgroups

subgroupG/H
centerC2×C4#14556124
commutator, cosocleC22×C4×C71C24
FrattiniC22×C4C23×D71
FittingC2×#407×C71C2
socleC22×C71#399
prime radicalC25×C71Q8
hypercenterC2×#407D71
hypocenterC71C2×#2091
LCSG ▷ C22×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#407

1102 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2272

Conjugacy classes & character table

2012 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 199315);