Finite Group Databasebeta

C8×D7×D8 #13323149

order1792
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC8×D7×D8

Splittings

FittingC7×C8×D8 ⋊ C2
SylowC7 ⋊ C2×C8×D8

Subgroups

subgroupG/H
centerC2×C8D4×D7
commutatorC4×C7C23×C8
FrattiniC42C23×D7
FittingC7×C8×D8C2
socleC22×C7C2×C4×D4
prime radicalC2×D7×D8C4
cosocleC42×C7C24
hypercenterC8×D8D7
hypocenterC7C2×C8×D8
LCSG ▷ C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C8 ◁ C4×C8 ◁ C8×D8

910 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, 138921);