Finite Group Databasebeta

C2×#22592039 #32165277

order18176
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC2×#22592039

Splittings

SylowC71 ⋊ C2×#2440

Subgroups

subgroupG/H
centerC24C23×D71
commutator, cosocleC23×C71C25
FrattiniC23C24×D71
FittingC22×C22⋊Q8×C71C2
socleC24×C71C24
prime radicalC25×C71C23
hypercenterC22×C22⋊Q8D71
hypocenterC71C2×#2440
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

3550 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9088

Conjugacy classes & character table

2036 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 337393);