Finite Group Databasebeta

C2×#22589636 #32025324

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

Aliases

direct productC2×#22589636

Splittings

SylowC71 ⋊ C2×#2052

Subgroups

subgroupG/H
centerC23#14556100
commutator, cosocleC22×C4×C71C24
FrattiniC22×C4C23×D71
FittingC22×#137×C71C2
socleC23×C71#121
prime radicalC22×#41×C71C22
hypercenterC22×#137D71
hypocenterC71C2×#2052
LCSG ▷ C22×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#137

1362 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9088

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, 197440);