Finite Group Databasebeta

C2×D7×#433 #14217509

order1792
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C27×C4

Aliases

direct productC2×D7×#433

Splittings

FittingC2×C7×#433 ⋊ C2
SylowC7 ⋊ C22×#433

Subgroups

subgroupG/H
centerC22×C4C23×D7
commutatorC22×C7C24×C4
FrattiniC2×C4C24×D7
FittingC2×C7×#433C2
socleC23×C7C23×C4
prime radicalC24×D7C2×C4
cosocleC2×C4×C7C25
hypercenterC2×#433D7
hypocenterC7C22×#433
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C22×C4 ◁ C2×#433

2310 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 448

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, 1033281);