Finite Group Databasebeta

C2×#11740621 #13521690

order1792
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC2×#11740621

Splittings

SylowC7 ⋊ C2×#2445

Subgroups

subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
Fitting, prime radicalC22×C7×#127C2
socleC24×C7C24
hypercenterC22×#127D7
hypocenterC7C2×#2445
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C22×#127

4110 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 896

Conjugacy classes & character table

244 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 337462);