Finite Group Databasebeta

C2×#22589667 #32025472

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

Aliases

direct productC2×#22589667

Splittings

SylowC71 ⋊ C2×#2057

Subgroups

subgroupG/H
centerC24D4×D71
commutator, cosocleC22×C4×C71C24
FrattiniC22×C4C23×D71
FittingC2×#340×C71C2
socle, prime radicalC24×C71C2×D4
hypercenterC2×#340D71
hypocenterC71C2×#2057
LCSG ▷ C22×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

1454 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18176

Conjugacy classes & character table

2024 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 197588);