Finite Group Databasebeta

C2×D7×#407 #14217224

order1792
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC2×D7×#407

Splittings

FittingC2×C7×#407 ⋊ C2
SylowC7 ⋊ C22×#407

Subgroups

subgroupG/H
centerC22×C4C23×D7
commutatorC22×C7C24×C4
FrattiniC2×C4C24×D7
FittingC2×C7×#407C2
socleC23×C7C23×C4
prime radicalC25×D7C4
cosocleC2×C4×C7C25
hypercenterC2×#407D7
hypocenterC7C22×#407
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C22×C4 ◁ C2×#407

7214 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 224

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 1032996);