Finite Group Databasebeta

C2×#11742958 #14262275

order1792
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C213

Aliases

direct productC2×#11742958

Splittings

SylowC7 ⋊ C2×#3504

Subgroups

subgroupG/H
centerC23C24×D7
commutator, cosocleC22×C7C26
FrattiniC22C25×D7
FittingC2×C7×#520C2
socleC23×C7C25
prime radicalC22×C7×#41C22
hypercenterC2×#520D7
hypocenterC7C2×#3504
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×#520

6958 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 896

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 1078047);