Finite Group Databasebeta

C8×D7×#41 #14218225

order1792
automorphism?
homologyAbelianization (H1) = C24×C8 · Schur multiplier (H2) = C29

Aliases

direct productC8×D7×#41

Splittings

FittingC7×C8×#41 ⋊ C2
SylowC7 ⋊ C2×C8×#41

Subgroups

subgroupG/H
centerC4×C8C22×D7
commutatorC2×C7C24×C8
FrattiniC2×C4C24×D7
FittingC7×C8×#41C2
socleC22×C7C24×C4
prime radicalC2×D7×#41C4
cosocleC2×C4×C7C25
hypercenterC8×#41D7
hypocenterC7C2×C8×#41
LCSG ▷ C2×C7 ▷ C7
UCSC1 ◁ C4×C8 ◁ C8×#41

2566 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, 1033997);