Finite Group Databasebeta

C4×D7×#131 #14217196

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

Aliases

direct productC4×D7×#131

Splittings

FittingC4×C7×#131 ⋊ C2
SylowC7 ⋊ C2×C4×#131

Subgroups

subgroupG/H
centerC4×C8C22×D7
commutatorC2×C7C23×C42
FrattiniC2×C4C24×D7
FittingC4×C7×#131C2
socleC22×C7C24×C4
prime radicalC2×D7×#41C22
cosocleC2×C4×C7C25
hypercenterC4×#131D7
hypocenterC7C2×C4×#131
LCSG ▷ C2×C7 ▷ C7
UCSC1 ◁ C4×C8 ◁ C4×#131

3366 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, 1032968);