Finite Group Databasebeta

C2×#22587360 #31969573

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

Aliases

direct productC2×#22587360

Splittings

SylowC71 ⋊ C2×#1613

Subgroups

subgroupG/H
centerC23#14556097
commutator, cosocleC22×C4×C71C24
FrattiniC22×C4C23×D71
Fitting, prime radicalC2×#534×C71C2
socleC23×C71#120
hypercenterC2×#534D71
hypocenterC71C2×#1613
LCSG ▷ C22×C4×C71 ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#534

1524 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4544

Conjugacy classes & character table

1586 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 141689);