Finite Group Databasebeta

C2×#11727690 #13381253

order1792
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#11727690

Splittings

SylowC7 ⋊ C2×#2035

Subgroups

subgroupG/H
centerC24C2×D28
commutator, cosocleC22×C4×C7C24
FrattiniC22×C4C23×D7
FittingC22×C7×C22⋊C8C2
socleC24×C7C2×D4
prime radicalC25×C7D4
hypercenterC22×C22⋊C8D7
hypocenterC7C2×#2035
LCSG ▷ C22×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C24 ◁ C24×C4 ◁ C22×C22⋊C8

1662 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 896

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 197025);