Finite Group Databasebeta

D4×#6379 #13369471

order1792
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productD4×#6379

Splittings

FittingC42×C7×D4 ⋊ C2
SylowC7 ⋊ D4×#104

Subgroups

subgroupG/H
centerC2×C4C22×D28
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC42×C7×D4C2
socleC22×C7C22×C22⋊C4
prime radicalD4×#1157C2
cosocleC22×C4×C7C24
hypercenterC42×D4D7
hypocenterC7D4×#104
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C2×C4×D4 ◁ C42×D4

1608 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 224

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 185243);