Finite Group Databasebeta

C2×#22592192 #32165364

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

Aliases

direct productC2×#22592192

Splittings

SylowC71 ⋊ C2×#2452

Subgroups

subgroupG/H
centerC24C23×D71
commutator, cosocleC23×C71C25
FrattiniC23C24×D71
FittingC2×#390×C71C2
socleC24×C71C24
prime radicalC23×D4×C71C22
hypercenterC2×#390D71
hypocenterC71C2×#2452
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×#390

3614 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, 337480);