Finite Group Databasebeta

C2×D7×#405 #14217185

order1792
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC2×D7×#405

Splittings

FittingC2×C7×#405 ⋊ C2
SylowC7 ⋊ C22×#405

Subgroups

subgroupG/H
centerC22×C8C22×D7
commutatorC2×C7C23×C42
FrattiniC2×C4C24×D7
FittingC2×C7×#405C2
socleC23×C7C23×C4
prime radicalC24×D7C2×C4
cosocleC2×C4×C7C25
hypercenterC2×#405D7
hypocenterC7C22×#405
LCSG ▷ C2×C7 ▷ C7
UCSC1 ◁ C22×C8 ◁ C2×#405

3518 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 448

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 1032957);